I would think that Anakin wins regardless of where he is. Neo fights hand-to-hand while Anakin fights with a lightsaber. Any Jedi who has his weapon in hand is more than a match for someone who is unarmed. Of course if Anakin lost his weapon Neo would whoop him, but I posted on the assumption that that doesn't happen.
Quick Take:
Neo: wears black
Anakin: wears black with armor and cape and sounds like James Earl Jones
ADVANTAGE: Anakin
Neo: Met and fell in love with Trinity
Anakin: Met and fell in love with Padmé, married her and now owns her jammin' booty
ADVANTAGE: tie (hey, both ladies are hot!)
Neo: hooks into the Matrix via hardwire
Anakin: hooks into the 'net via Apple's Airport Extreme
ADVANTAGE: Anakin (Think Different!)
Neo: main transportation is a beaten up hovercraft
Anakin: Jedi Starfighter, TIE Advance (later on), that yellow speeder he 'jacked on Coruscant (thief!)
ADVANTAGE: Anakin
Neo: memorable line: "Whoa...."
Anakin: memorable line: " The Jedi turned against me; don't you turn against me!"
ADVANTAGE: Anakin
Neo: pretty much a weakling outside the Matrix
Anakin: whatever you do, don't call him 'Ani' when he's mad (only Padmé can do that)
ADVANTAGE: Anakin
Neo: built a strategy to defeat Agent Smith
Anakin: built a protocol droid that doesn't know when to shut the hell up
ADVANTAGE: Neo
Neo: Coolest Moment= lobby shootout
Anakin: Coolest moment= On Bespin, Han shoots at him, deflects laser bolts with his hand, grabbed the gun from him via the Force, then sat down and finished his dinner. Now THAT'S awesome!
ADVANTAGE: Anakin
Winner for this round: ANAKIN!