If it is actually a war, legally declared as one, then the rules of war apply. The Geneva convention must be followed, and the principles of a Just War. Osama would have been an enemy combatant, and there are rules about how these must be treated. But nobody has declared war, because they would have to follow these rules if they did so. Therefore, the rules of civilian engagement still apply, and Osama bin Laden was executed because it played better than capturing him. Those responsible treated life as cheap.
If it is a war, then the rules apply. We do not execute enemy soldiers without a trial: we kill them in combat, or we capture them. If it is not a war, then the terrorists are just another category of criminals, who should be pursued, arrested, and tried in criminal courts. There are arrangements for criminals who act across borders. It is entirely possible to extradite such prisoners and lock them securely away.
And no, I do not think he should have been killed, if he could be captured (and it seems pretty evident that he could have been). Life is sacred. We do not convince people of this by acting as if some life is disposable. We do not convince ourselves of this by acting as if some life is disposable. God wills all souls to come to Him: what a statement it would have been, to treat Osama as if his life was sacred, even after the death he caused. Do we not teach that every sin can be forgiven?