Strider (Aragorn) vs The Man In Black (Dread Pirate Roberts/Westley
Round 1: each are given a standard hand and a half sword (we'll assume that Aragorn is used to wielding a longsword and Westley a rapier)
Round 2: each are given their standard equipment and weapons
Round 3: each have their bros for back-up - Aragorn has Legolas and Gimli, Westley has Inigo and Fezzik (nobody has any weapns) straight brawl
Round 4: each must give a rousing speach to stir their men to victory in battle, which can inspire their troops more effectively?
Bonus Round: (resuce the girl) each have taken the others' lady captive and hidden her in their homeworld - Aragorn must rescue Arwen from Florin and Westley must rescue Buttercup from Middle-Earth (this is done simultaneously so neither can directly impede the other's progress) who locates and saves their girlfriend first?
Plot-twist Double-Bonus: the ladies each free themselves and find a (non-magical) horse, which of them rides to freedom and reunites with their dashing hero first?