They would have to execute him quick if either country held him. Unlike Iraq, most of the major players in the UN support our efforts against Osama, and while they may not be militaristic in nature, there would still be reprecussions against anybody harboring him (probably economic in nature). Many in the UN are truly afraid of Osama and his followers, because the Al-Q are actively working in many countries against those governments.
Iran can't afford that at this point, and everything Saudi Arabia has done to show that they are our "friends" would be wiped out in a heartbeat. The American people seem to have bought the "Saudis are our friends and allies" thing, but that would go out the window.