I voted LotR first... but I would change my answer to Thrones because of the white walkers. This is how I see the battle going down... It would start and LotR would decimate since they have superior magic, beasts, and armies. Thrones would see the majority of their populace decimated... BUT that would only make them stronger BECAUSE of the the White Walkers. These guys would just start resurrecting the fallen, adding them to their numbers. Since they can only be defeated by dragon glass (which no one in LotR would know about since only 3-4 people in Thrones even know it) the White Walker army would just start taking down LotR soldiers/mages/beasts by shear numbers alone. Every living being that would be killed would join there side and add to their numbers with no way to stop them.
The key here is the assumption that only Dragon Glass can kill White Walkers and there is no other way to stop them. They would just spread like a plague and win by shear undead unstoppable numbers.