It simply comes down to Paul and (Early)Gary Mother<BLEEP!>ing Oak. Now then, while both show some very similiar personalities, there is a difference.
Paul, on one end, simply didn't want to be second place. He wanted to be the best, and he wasn't gonna have ANYTHING stand in his way. This is one reason why I hope The Pokemon Company bring Paul back. He is simply Ash's complete opposite... Kinda like Ying and Yang... Heck, Ash, for a while, simply became better just because of Paul.
Gary... Let me just say this: There is a reason why people call him Gary Mother<BLEEP!>ing Oak. No matter what Ash did, Gary was first. Get a badge? Psh. Gary probably already had three. Get six badges? Gary already had eight. Get all eight badges? He had freakin' TEN! O.O He even caught more Pokemon than Ash did, and, in my opinion, had one of the coolest Pokemon teams ever in the series. Heck, the Charizard vs. Blastoise battle in the Johto saga is still ranked as number three in my Top Five Matches of the Series.
So... Who wins? Both. ^.^