Allow me to use my humble skills of analysis to analyze many of the claims being made here. First, I have to offer a few analyses before I go onto my own argument.
P. 1. This is not an issue of one question.
The issue at hand is more complex than simple issues of whether this is that way or not. We've all been touching on the subject, but I think it needs to be carried, screaming into the daylight. As far as I see it, there are two issues at hand. The first is whether or not what Kirk did was ethical in any sense. That is, were his actions 'right' or 'wrong'. The second issue is whether or not what Kirk and crew did was internally consistent within the characterization of himself in other Trek media. This is important due to a simple issue of Subject-predicate logic.
P. 2. Was what Kirk did ethical?
To even touch upon this discussion, we must make a few basic definitions. The first is "what" ethics is. Ethics, in an academic sense, is simply the study and reflection upon our own moral actions. Now, what is morality? Morality are the 'ideas' of right and wrong, good and evil which we have constructed via our experience and socialization(or innate ideas, go to hell Descartes :P). Hence, Ethics is the study of how to achieve 'moral' actions, that is how do we become 'good' or do 'good'.
Naturally, there is another issue at hand here. There are essentially an incalcuable number of ethical standpoints all throughout reality if you consider the argument that each and every person has their own unique version of Ethics which they abide by. So then how do we determine whether the action is good or bad? Well, many times we can reason it out like Kant did, but others are more content to leave it to religious 'revelation'. So then how do I even consider advancing in this line of discussion with so many ethical positions? Well, I'll analyze several ethical viewpoints briefly, and then place emphasis upon one of them in particular.
I'll start with the one undoubtedly people will want to look at the most, judging from the earlier responses. Egoism. Egoism is the ethical stance revolving around gratification and development of the 'self'. That is, a person who acts only towards their own benefit and interest. Ayn Rand, and Nietzsche are main proponents of this system of ethics. The question here is rather simple. Was Kirk and crew acting to benefit themselves primarily? I think it's plain, as judging from their reactions, that they were in fact acting for their own pleasure. They wanted revenge, so they took it, even though Nero was going to die anyway.
Utilitarianism is similar to Egoism in the sense that it revolves around pleasure, both my own and the pleasure of others. Though, if we look at Jeremy Bentham's Utilitarian Calculus, only one actually takes into consideration other people. In my opinion Bentham's Utilitarianism is really just another form of Egoism. However, other Utilitarian concerns, including Bentham's, include the point of the "Greatest Pleasure", to the "Greatest Number". So in this case we have to wonder; was Kirk acting to bring the "Greatest Pleasure", to the "Greatest Number"? In the way he acted, I am willing to say no. By killing Nero in an anonymous, ignoble manner he deprives the rest of the Federation from the 'pleasure' of satisfaction. That is to say, because Justice has not been 'done', they will not get the pleasure of seeing Nero tried, and then eventually executed. As well, his actions did not necessarily prevent Nero from causing other harm to other people in the future, as there are other actions which could have had a similar effect. For instance, there are two considerations here. The first is that Utilitarianism is only concerned with the consequence of an action. That is, whether it has a direct causal effect upon creating 'more' happiness. The second is in another point, Utilitarians usually emphasize the value of the law, and actions which unnecessarily break the law are considered to be negative effects. The Utilitarian argument is rendered moot, I think, based upon how you consider it. The situation can be considered here in two ways. One; Kirk killing Nero causally brought more 'pleasure' to the universe by preventing him from potentially going back in time(This is also contingent upon that very same point, whether Nero would have been able to go back in time again). Two; Kirk killing Nero did not causally bring more 'pleasure' to the universe. This point is based upon the potential lack of popular 'satisfaction', and the possibility that Nero's vessel would not have survived the black hole, as damaged as it was. Personally, I feel that the second possibility is a little more likely in this situation.
The third viewpoint I'll analyze is called "Deontology". This system can be summarized as being about actions done "because they are right", and "bound by duty, as if they were natural laws". This philosophical system sets the bar rather high, as opposed to setting it rather low like Utilitarianism or Egoism. Actions, first and foremost, are made moral not by the outcome, but by the intent behind them. For example, if Kirk were killing Nero in a sort of 'mercy killing', it could potentially be considered correct. However, at this point the most important thing to do would actually have been to rescue Nero, and then place him under arrest despite the potential damage to his vessel. Again, Deontology is not about outcomes. When confronted with a situation which could spell doom, and Duty dictates that you still face such a fate, the good Deontologist will ultimately act in such a manner.
Now, why is this last point so important? We've already established that at least by one ethical construct approves of Kirk and co's actions. However, Deontology in some form is in fact the binding, pervasive philosophical structure of the Federation and in fact Star Trek as a whole(Removing such a thing falls into a problem, as per P. 3). Things are done because they are the right things to do, not because of consequences or self-aggrandizement. For example, the Prime Directive in Star Trek is only violated when there are other concerns, other duties which supercede it come into play. This would render the Federation as having a form of Rossian Deontology. The Federation, and in fact Kirk as an individual, are Deontological to at least some extent. For Star Trek as a whole, I think the best example is TNG episode "Where Silence has Lease", when Picard refused to sacrifice one third to one half of his crew due to the innate 'wrongness' of using his crew like that. Another example is in TOS episode "Who Mourns for Adonais?", where Lt. Palamis chooses Duty over personal self gratification. Yes, this message is even present in the Original Series. They are plainly not Utilitarian(The majority would likely survive the encounter), nor are they Egoist(There was no effort to self-aggrandize or work towards ones benefit).
P. 3. Was what Kirk did internally consistent with other Kirk portrayals?
This is a more touchy issue, as well as being more of a corollary, but I primarily want to discuss why this question is important before we go on to analyze the actual issue. Why, then, is it important if this Kirk is matching that Kirk's portrayal? In short, this has to do with the issue of identification in Subject-predicate logics.
The Law of Identity states thus; Something is, what it is. Or more simply, A=A. Now, in subject-predicate logics, this means that we can identify A by the sum total of its predicates. For instance, I know this chair is my chair because it shares the predicates of what I recognise as being 'my chair', from color, to shape, to position in my room. To be more precise, then, A=A1, A2, A3, A4, A5, and so on. Any such list will be quite large at times(Which promps Metaphysicians such as Leibniz to state only "God" could figure out a list like that). To bring us back on course, this means that to identify "Kirk", he has to have the predicates of Kirk. That is, shape, size, voice, personality, etc. Other Modern philosophers like John Locke, however, have made it clear that we can't identify a person with their body, so we can discount physical differences. Besides, this is supposed to be Kirk at a younger age, so we can accept physical differences. So then we have to look at the qualities of his personality, the true defining feature of a person.
Why is this line of digression important though? Simply, because if ST11 Kirk does not fit the predicates of TOS Kirk, then he is not that Kirk. He may have the same name, shape, and he may be intended to be a different form of the 'same character', but he would not be the same Kirk. This would be like two twins, each named John Smith. They may look, walk, speak, and on a genetic level be intended to be the 'same person', but if there are distinct differences (IE; spatial location, experiencial history, personality), then they are not the same person. Naturally, as we're dealing with a fictional character 'spatial location' isn't as much of an issue. However, despite both John Smiths having similar attributes, having the same name, and being made from the same 'source material', they are plainly not the same person. Consider a more stark example. There is a man named James Mills. There is another man named James Mills across the country. By simple virtue of their name, they are not the same person.
Now, to bring us back in line again, ST11 Kirk is to be expected to have less in common with the TOS Kirk. He is, after all, supposed to be a 'younger' Kirk. However, certain fundamental things should still be there, though in less refined senses. However, in that same breath, he cannot be too dissimilar, because then he fails to meet the necessary predicates to be identified as "Kirk". He then becomes another, different Kirk. An entirely different being. For example, we recognise Mirror-Kirk from "Mirror, Mirror" to be a different Kirk from a different timeline because his predicates are different. We can't appreciate the relationships the Original Kirk had through this being, because this is an entirely different Kirk. I find this especially hard to accept because this 'new' Kirk is not intended to be a 'mirror' Kirk at all, but merely the 'same' Kirk thrust into an alternate time line.
This then means that if the predicates differ from the source material, he becomes a different character. He cannot be valued, nor can any of the characters be valued, as the crew that we know and love. The effect of ethics upon this is thus; he is then excised from the moral constraints of the "Original" Kirk. He can then act however he wants as an original character, which opens up a slew of other issues, chief among them the reason for enjoying the movie, which I won't go into at this point.
Now, the problem is that I don't think he really does act in a consistent manner. The original Kirk was individualistic, confident bordering on prideful, but still largely in control. This 'new' Kirk is completely out of control, without the charm or cunning that the 'old' Kirk had. I find it hard to believe that he would see so much development from when he was 25, to when he was 31 when he became the captain of the "Enterprise". As well, he's vengeful, even against an enemy who is ultimately weak and defenseless. This is not what Kirk would do(See TOS: Arena). There are likewise distinct differences in their approaches to issues. 'Old' Kirk approaching them based upon principle and personal pride, and 'New' Kirk, who seems to exist solely upon impulse and self gratification. Even when 'Old' Kirk borders on actions of the 'New' Kirk, it's always when his emotions have gotten the best of him and broken down his rational sense. It's a flaw, there, not a virtue as demonstrated by ST11.
That's enough for now, I'll post this and then work on the rest of my argument while you guys read. :>