When answering this question, I also need to consider the consequences of either person's death.
If I died, how many others out there who need my help, either on a personal or professional level, would have to suffer? Could I have much more to offer to the world? Could I save or change more lives for the better or for the worse? Is all that worth my sacrifice?
I can see a degree of selfishness about it all. Is it selfish that I choose to live so that I can fulfil my personal agenda to help others - something that is not even guaranteed, and which could backfire spectacularly? Is it selfish that I throw it all away and die in a state of personal contentedness to help just one person regardless of the countless others who could benefit from me?
How would I react if I lived and the other person died? Would I be full of remorse over the death of the loved one I should have saved, that I just stop everything I do and enter a prolonged period of mourning? Or will it add a new-found drive that I've been given another chance at life?
All of the above of course also applies to the other person in question, whether they lived or died instead of me, and whether they would do the same thing to me.
If I had no time to think about it, though. then I'd go with my gut instinct. I feel that the point about living with the knowledge that I denied someone's continuing life, so that I could further my own, would have a great effect on me and would haunt my every decision afterwards. Rather than consider their sacrifice as a gift and a means to drive myself further, I'd still see it as a burden in that they could have done something with their life instead of me (though there is still no guarantee of this). Therefore, my default answer, with the best of intentions, is still YES.