Gotta go with Star Wars (even though SW arc types and story borrows heavily from LOTR)...
Let's break it down shall we:
Round 1: Heroes
Frodo vs Luke - uh, tie - they both suck...
Merry & Pippin vs C3P0 & R2D2 - The droids win, other than hanging out with trees, what else do M&P actually do?
Aragon vs Han Solo - Tough one here, They're both cool, they both bang the hot chick at the end...
Han has Chewie though and Aragon has stupid Legolas so Han wins
Plus Han gets frozen in carbonite while Aragon just falls off a cliff (which didn't even happen in the books).
Gandalf vs Obi Wan Kenobi - Gandalf is clearly the winner here, dude kills the balrog where Obi Wan takes one lightsaber to the chest and he's a stupid ghost for the next two episodes...
Winner this Round: Star Wars
Round 2: Villains
The Witch King vs Darth Vader - Gee, I wonder who's going to win this one... Lets see, Vader is the ultimate movie villain and the Witch King (while he is a badass) only has a real presence in the last movie. Vader wins and force chokes the Witch King for good measure.
Sauron vs The Emperor - I'm giving this one to the Emperor because he actually does stuff. Other than being this great big eye, what else does Sauron do exactly?
Orcs vs Storm Troopers - This one goes to the Orcs, both opponents are pretty useless but the Orcs seem to do more damage and look a lot more intimidating...
Winner this Round: Star Wars
Round 3: Locations/Transportation
Walking/Horses/Boats Vs The Millennium Falcon/X-Wing - Duh!
The Battle For Minas Tirith vs The Battle For The Death Star - Another toughie... I'm going to call a tie on this, Minas Tirith was truly epic but the Death Star battle happens twice that's how awesome that place is...
The Prancing Pony Vs Mos Isely Space Bar - Gotta give this one to Mos Isely, it had the freaks and the funky music
The Shire Vs Tatoonie - I'll give this one to the Shire, it's much nicer
Winner this Round: Star Wars
Overall Winner: Star Wars