I will answer this question by specifying what is meant by a morally committed Kantian and Utilitarian and interpreting their required behavior in several hypothetical situations. These situations should reflect possible circumstances I could actually find myself in if I was stranded on an island with another person. The hardest aspect of this question may be in staying serious enough - staying away from models which are so contrived that they cease to be relevant to the question.
The Utilitarian, according to the theory’s strictest sense is bound to maximizing overall well-being. I will take well-being to loosely mean something along the lines of happiness. This interpretation is most commonly agreed upon, so it should serve for our purposes. I will try, however, to keep in mind that a distinction between different schools of utilitarianism may break arguments against the Utilitarian, and will points them out if needed.
The Kantian is bound to a less concrete principle. She should never treat other people merely as a means, but always as an end in itself. Although there are other formulations of Kant's moral theory due to its ambiguous nature. To simplify things, the heuristic laid out at the start of this paragraph will serve as the working definition of Kantian moral theory.
In reference to the different scenarios I alluded to in the introduction I will try to extrapolate what kind of models could guide us in the right direction. On a deserted island there should be a discrete set of aspects to be valued. Put more plainly, there are only a few things that we would really need for survival - seeing as that is the goal of our presence there. We would definitely need nutrition. Water and food are essential for human survival. A little less important yet vital thing we need is shelter. Knowing that these are the only things that are necessary for survival, they are the only objects of value that should be discussed in relationship to me and my morally devout ‘friend’. These can give us an idea of what sort of situation we should focus us on to distinguish the potential companion’s behavior..
Sharing, as a principle, seems to be relevant to emphasize different courses of action that each version of the companion would take. The Utilitarian would act in a way that benefits me knowing that he should take my well being into consideration when acting. He has to include me in our needs for nutrition and shelter as he has to consider me too in his moral calculation. A devout Kantian can never merely use you as a mean. So at least he cannot use you merely to gain nutrition or shelter, like killing you for food or skinning you for a coat. However, it seems that he is not obliged to help you. After all, if he sees you starving in front of him, he still has not merely used you as an end - as he did not use you at all! So, considering how each agent would act in a situation where you want them to share, the Utilitarian seems like a much more compelling companion.
A devout Kantian would probably take to heart that he is an inadequate island companion and would try to refute this claim. A common attempt for Kantians to consolidate their maxim of ‘means instead of ends’ is to make a distinction between what is usually thought to be the end and what they think it really is. In this case, the Kantian could do so by stating that not helping someone who can only be helped by you is using that person merely as a means. Namely as a mean to survive. By just ignoring someone who has survival needs, you are effectively using them as a means to survive instead of an end. But what compels the Kantian to believe that not helping someone who is in need of your help is actually using them as a means? Even if you are the only person in the position to help, there is nothing in Kantian laws that state that one should help people who require your help for survival. So the Utilitarian seems to have the right to stomp his feet on the ground at this point and demand that the Kantian explain himself further.
One separate problem that I have with being on a deserted island with a Utilitarian is that his moral guidelines allow him to deceive me. In combination with the goal of maximizing overall well being, this can allow for some unnerving circumstances. For example, assume that my Utilitarian companion is a Hedonist and believes that overall pleasure should be maximized no matter what. After all, doing so is morally right. Unfortunately, he might conceive of an elaborate scheme in order to kill and eat me while staying within the confines of his moral beliefs. So he tells me that he decided that he should kill himself based on his morals. Maximizing pleasure is the right thing to do, so by killing himself he can provide for me by leaving me his body - allowing me to survive and giving me the opportunity to feel pleasure at some point in the future instead of being dead where no such emotions can be felt. He tells me that he has to do this because it is better for one person to live than none. So I follow him to the cliff (to gather the fresh flesh) where he says he will jump off of. Instead of jumping, he flings me off the cliff and watches me fall to my death. He did it exactly for the reasons he stated to me previously, just that he deceived me so I would feel pleasure (of hope) until I died. His justification for killing me instead of killing himself is that he could not have been deceived (as he came up with the scheme in the first place) and so, would not have been able to feel pleasure up to the point of death (knowing that he would die). So, basically, I can think of examples where the Utilitarian should be inclined to deceive me in order to survive, while being justified under the premise of maximizing global well being. The Kantian, on the other hand, is not allowed to deceive me because that would involve using me merely as a means instead of an end.
The Utilitarian might add at this point that “calculations” are unreasonable to perform before acting. As this claim does carry some weight, secondary rules are usually alluded to in their stead for moral guidance. Secondary rules are sorts of summaries and heuristics that can be used in the moment whereas “calculations” are done in retrospect. Considering this, the Utilitarian might claim that secondary rules would not allow for deception. I think this is arguable, but that it would ultimately fail. After all, the question of where the secondary rules came from has to be answered by some kind of reference to Utilitarian principles of well-being. So it seems plausible that after all there would be a secondary rule that endorses deception in certain scenarios.
A slightly unrelated but independently important point on the Kantian agent is that his apathy towards me may come in varying degrees. In other words, just because the Kantian is not morally compelled to share with me or help me, he might do so anyway. I think this aspect is important until you reconsider that you are stranded on an island. People are survival driven animals, and so their outlook on empathy changes as death comes nearer. It seems to me that even the most empathetic Kantians would succumb to their base desires in the moments where you would want them to help you most.
So far it seems that I have reasons both for and against either versions of my potential companions. The Utilitarian would help me, but is compelled to deceive me to further his survival. The Kantian would never deceive me, or use me in any way, but would be justified in helping himself over me. I think it would be most beneficial for me to use the Utilitarian to further my survival as long as possible by making him work with me and share food at first. At one point it would be within his moral imperative to get rid of me as he would realize that I am deceiving him for my benefits. Once this point occurs I would kill him for food and tools in order to ensure my survival. Intuitively this screams of immorality but this is not my goal; it is survival.
So, to conclude, it seems that a Utilitarian would be a better companion than a Kantian for a survival-driven person like me. However, because I am survival driven I instantly consider the possibility of killing my companion. For that reason I prefer the Utilitarian because I am ready to dispose of him when necessary. For a more passive (or weaker) agent, the Kantian would be preferable because, even if he may not help you, he would not engage in conflict with you. Therefore, it depends on the person and the whether you assume an aggressive or defensive (team-work oriented) approach to your survival and how devout of a moral agent your companion is.