They had this same question on that discovery/learning channel show (don't remember the name). The Lion won based on the following facts:
-Tigers are solitary creatures, and hunt occassionally when they need food. Lions are pack animals; male lions are raised from birth to fight other lions in order to defend their pride and such. Thus, lions would have more experience with a large, ferocious opponent.
-Tigers tend to use a neck bite as their main method of killing. Lions also use the neck bite, but are more prone to use claws as well. The lion's mane would help in confusing the tiger enough to perhaps make it miss its first attempt at a neck bite, giving the lion an upper hand
-Tigers are larger and stronger, but as previously noted, the Lion's much greater experience in combat with other large cats was thought to outweigh this factor. Basically, both cats are strong enough to kill one another with a single bite, or a well-place claw strike. It would come down to which animal made for itself the first killing-blow opportunity. The lion was decided on as the winner.