The Ash/Paul rivalry was about mutual respect, or the lack thereof. The rivalry ended with both trainers respecting one another and understanding that the others method could be effective at raising strong Pokemon. This was shown by Paul acknowledging that Infernape was very strong, and telling Ash it was a great battle. Paul also acknowledged that his training methods wouldn't have worked very well if he'd kept Chimchar, and that going to Ash was the best thing for it.
Paul left with a new attitude that didn't drastically alter his personality to the extreme that it seems like he's a different person, but still had a more postive outlook on training and his Pokemon.
Seems like it got good closure to me.