Good question, but I really don't care. In fact, I'll go so far as to say that I don't care if we never do. I can't think of a single good reason to capture or kill the man. I suppose the argument could be made that we as a civilization need to feel that he has been brought to some sort of justice. Unfortunately, I'm of the opinion that capturing or killing him won't help, and if anything will make matters worse.
Here's my thinking: No mater how we get him, he's instantly a martyr. Killing him is a worst-case scenario. Gloating over is death will re-vitalize an enemy at a time when it looks (on the surface) like we're starting to make some progress.
What if we capture him? Then what? A trial? I'm no lawyer, but I can't imagine that this is an open-and-shut case. At least not in the sense that we normally think about it. There's probably very little admissible direct evidence linking him to the events of 9/11. Maybe we could get him on tax evasion charges...
No, I like Osama right where he is, probably in a cave somewhere, living out the last days of his miserable existence.