Well, this is certainly a question that has been on my mind, and the minds of a lot of other people as well recently. These are both very powerful polities with the potential to pour out tremendous havoc on one another and, at least as importantly, could destabilize the entire region and draw many bystander states into the conflict as well.
Hmm. I think I have settled on an approach. I'm going to begin by looking at both Israel and Iran separately, analyzing their different attributes and historical behaviors to see how likely they are to find themselves drawn into war. Then I'm going to look at their dyadic relationship - in other words how those variables might interact. And I'm going to do this one variable set at a time.
Important: war is war. War is not terrorism, nor is war assassination, nor is it any of the other types of political violence - and there are many. War, as political science today understands it (and as I defined it in my college honors thesis on the Platonic nature of warfare) is mass, organized, explicit violence with a specific ends between two or more polities. Will Israel and Iran continue to engage in violence against one another? I'd say 99.9999% yes, because saying 100% is probably a no-no. But that is a very, very different question than, will Israel will go to war with Iran, or vice-versa.
Alright - to it then.
Once upon a time most people assumed that all states behaved similarly in their international relations, regardless of their internal institutional arrangements. After all, respective to one-another, all states seek the same things: they wish to survive, increase their relative power, and maximize their benefits from international relations while minimizing benefits to their opposite numbers. We still believe that, to a substantial degree. Then along came Immanuel Kant and we began to really question, for the first time, whether or not this was true. He really wrecked it. You see, Kant devised a plan for perpetual peace - a set of conditions that he believed would result in an end to interstate warfare. Among these conditions was Kant's requirement that all of the states in the world system have a republican form of government.
Since Kant wrote, we've been looking into this - do the internal characteristics of states affect their external behavior? And what we found is, certainly they do. They do so for a number of reasons, as well - reasons which, when you consider them, really make a great deal of sense. For instance - imagine a political system in which the manner people get into office is through peaceful means - oh, they may lie, steal, cheat, and sneak to do it, but they do it without overt violence. Well, that means that the skill set brought to the international relations table by these leaders will be one which does not inherently depend upon the generation of bodies. Since people try to negotiate and operate within a construct that takes advantage of their particular skills, it wouldn't be surprising if such leaders would seek peaceful, rather than bellicose, means of getting what they want.
We have also noticed that trust is higher bestween certain types of states than it is between others, due not only to shared values, but also to shared means and rational assessments of the the likely strategies and tactics to be taken by their peers. Finally, we have noticed that in free states in which rule of law is well established the people tend to have a restraining effect on their leaders with regards to their leaders - after all, free states are better able to calculate the real costs of war and in all states the burdens of warfare fall disproportionately on the poor and middle-classes.
All this said, the standard wisdom today goes as follows: (1) free (stable democratic-republics) states rarely if ever fight other free states; (2) when free states fight unfree states, as long as the war is under five years in length, they tend to win at least in part because of their superior resource allocation capabilities and higher morale and legitimacy; (3) free states may be less bellicose than authoritarian states, but both are definitely less bellicose than anocratic states (states which have characteristics of both authoritarian and liberal states).
Okay - so where do our states fall? Well, I turned to the Polity IV project - an effort to compile data on where every state falls in the spectrum between democratic and autocratic. What I found is illustrated here:
Note - I think it is worth observing that Israel, while it is democratic, is also problematic in terms of its overall liberality due to its treatment of the Palestinian people and its tendency to obey agreements with them and its Arab neighbors largely when it is convenient (I am not absolving the Palestinians of their particular role in the violence of the area, mind you, but nonetheless, it warrants note). This may be speculated as potentially resulting in higher cultural toleration (either general or among elites) for the use of violence as a method of achieving political goals, thus making Israel more prone to bellicosity than a perfectly functioning democracy. Furthermore, Israeli policies alienate Palestinians, adding energy to a cycle of violence which clearly has the potential to justify interference from outside political actors - Iran included.
Something else poltiical scientists have observed is that states which have fought many wars in the past are more likely to use war as a strategy than those which have fought few or no wars and, similarly, pairs of states which have fought one another in the past are more likely to do so in the future than those which have not. The first of these speaks to cultural trends and also to the fact that causal conditions that led state X to war in instance A are unlikely to have disapperaed by instance B or instance C. The seonc of these speaks to two facts - first, states which have fought often generate reasons to fight each other again in the course of fighting or negotiating afterwards, and secondly states typically fight states which are near each other - and of course ever state has a finite number of states within fighting range.
In order to make some statements on this I went to the Correlates of War project and looked up, in the simplest of terms, just how darn violent Iran and Israel are, respectively and in reference to one another. Note that here I'm just looking at interstate warfare - there are a lot of types of violence, but I'm limiting myself to the bounds of the question.
Well, first things first: Israel is, in terms of interstate warfare, more violent than Iran. Iran has been involved in only events which can definitively be categorized as interstate wars since the early 19th Century - the 1856 Anglo-Persian War in which Persia attempted to regain control of Herat from British-dominated Afghanistan and the Iraqi-Iranian War of the 1980s which began with a massive Iraqi surprise attack on Iran but ultimately ended in stalemate. I consider at least one other conflict, at minimum, to be worth noting in the same stroke - the joint Anglo-Soviet invasion of neutral Iran in 1941. On the other hand, in Israel, we have the First, Second, and Third Arab-Israeli Wars of 1948, 1967(sometimes called the Six-Day War), and 1973 (sometimes called the Yom Kippur War), as well as the 1956 joint Israeli-British-French invasion of the Sinai Peninsula and takeover of the Suez Canal, the Sinai War of Attrition begining in 1969, and the 1982 intervention of Israel in the Lebanese War.
What can we say about this? Well, first, Iran not only has been in fewer interstate wars, it hasn't started any since 1856, and even that war may be considered an anti-colonial war. Secondly, Israel has fought a lot of wars, which matters even more given that it didn't exist in an any way recognizable form until the late 1940s. Further, we can say that while certainly Israel hasn't started all of its interstate wars, did start the Sinai War and the Second Arab-Israeli War and its decision to intervene in the Lebanese War, in response to Palestinian Liberation Organization attacks on Israeli targets from safehavens in Israel, must be considered at least partially an offensive action. We can also say, however, that Israel and Iran, while they have certainly carried on allegorical wars of rhetoric and carried out extensive non-militarized violence against one another, their actual military activities against one another have been limited to the point of virtual nonexistance.
Ultimately, Israel and Iran are both powerful, but mid-level states in their capabilities. I would recommend you check out an article by Al Jazeera's "Iran and Israel: Comparing Military Machines" by Ben Piven. I won't sing a song already sung, but I will make some observations:
(1) Neither Israel or Iran have a legitimate capability to in a conventional ground-assault war, even one enhanced by air and naval capabilities, against one another, if for no other reason than the Arab states that lay between them are unlikely to support any such action.
(2) Iran has specifically pursued capabilities meant to offset the high-tech, logistic-driven military capabilities of modern, Western-style militaries. This means that while Israel has superior technology, without massive American support (and perhaps even then) its forces would be strongly challenged by the Iran's anti-air and anti-armor capabilities, as well as its extensive infantry-based response plans, would potentially result in a stalemate should Israel try to attack Iran en masse. This also reveals something else - it is highly unlikely, given the asymmetry of the of their forces that Iran's primary focus, at least for the time being, is offensive capabilities.
(3) Nuclear capabilities are entirely assymetric. Iran does not have a nuclear arsenal, and even if it achieved nuclear status in the next several years it would be radically inferior both quantitatively and qualitatively to the Israeli force which, while unofficial, still is assumed to number over 200 warheads, of which at least some of which are assumed to global-target capable, since it is assumed Israel has intercontinental ballistic missle capabilities. This is a credible deterrence of the highest order - to attack Israel with a weapon of mass destruction, or with a conventional attack that threatens the survival of the State of Israel is to virtually guarantee any nation unacceptable losses from a nuclear counter-assault and/or the tactical application of nuclear weapons. It is difficult to imagine, then, that Iran would engage in full-scale conventional war against Israel in the foreseeable future for exactly this reason. Yet this asymmetry means that Israel is able to attack Iran with near impunity (at least as far as military assaults may be concerned). Ironically, then, it may be that we can say that the chance of an Israeli-Iranian war would likely decrease in the event of Iranian nuclearization, as this would result in a balance-of-power based upon the tyrannical logic of weapons of mass destruction, though the consequences would likely be tremendous.
Sanctions are a form of violence - let us not pretend otherwise - but they are clearly short of outright warfare. In the globalized political-economy sanctions play a role not unlike that of seigeworks in premodern political-economies: they aim to starve, literally and allegorically, either the elites of a polity into submission or the general population into rebellion. The Council on Foreign Relations has compiled a list of current American, Canadian, European, and international sanctions (as of July) levied against Iran over their progress towards nuclear weaponization that will illustrate the scale of the current seige. How have they worked? Well. That is complicated. The rial seems to be collapsing, but the Iran seems to be continuing their efforts to develop nuclear weapons. My suspicion is that, unless Iran experiences a successful liberal revolution (which I don't foresee in the near future), we can expect the sanctions to fail - Iran is going to pursue nuclear weapons because they see (probably correctly) WMDs as the simplest means of detering Israeli, Western, Russian, Arab, and possibly south or central Asian military intervention or efforts at regime change.
Prognostication is dangerous, and in the case of warfare it is supremely dangerous. Nonetheless, let's give it a whirl.
First, I want to point out I did not take into account rhetoric. Perhaps that is a mistake, but setting that aside was a choice that I made in the interest of avoiding emotional biases.
Second, I would say that the regime data is inconclusive, but destabilizing - the imperfect liberality of Israel and the autocracy leaning towards anocracy of Iran certainly isn't helping the situation. Furthermore, the relationship between Palestinian disestablishmentarians and Iran serves as a near-permanent casus belli for both Israel and Iran.
Third, I would argue that the historic trends, combined with the nature of the asymmetric capabilities of Israel and Iran, indicate that the chances of an Iran-initiated war are fairly limited (again, remember I am talking about war - terrorism and other forms of violence are an entirely different subject), but the chances of an Israeli strike are hardly insignificant. Should Iran successfully demonstration both (1) nuclear weaponization capabilities and (2) warhead delivery capabilities than interstate war between Israel and Iran becomes virtually unthinkable, however.
Finally, sanctions are unlikely to achieve their desired effect, in my opinion. Indeed, I would argue that they are pursued so consistently in order to legitimate a possible future use of preemptive force in the form of air strikes or war against Iran by a Western or Western/Arab coalition, though the undesirability of such a conflict makes it rather unlikely in the near future.
Prediction: I believe that, given the evidence the chance of an Iran-initiated war against Israel is incredibly low, but that while it is still unlikely, the chance of an Israel-initiated war against Iran is significant enough that, were I a key American, European, or Arab leader I would make it a key point of policy to make it clear that such an Israeli policy would entail incredible costs and risks with comparably low benefits.
At least that is my two cents.