I don't think they'll throw Paul in again. The abandoned-and-eventually-caught-by-Ash Fire-starter formula has been here for a long time (Torchic is an exception because May took it), and they're just using that boring plot device again.
Anyway, back to the main question. : D
Despite the appearance (esp. hair) explicitly screaming Paul, I think Trip screams Gary instead with his character. Paul was just plain cruel to (almost?) everyone - and frankly I don't like his character, although his rivalry with Ash was pretty amazing. Trip, on the other hand, didn't have much conflicts against other people except Ash, was always one step before Ash, and either owned or tied with Ash. Gee, where have we seen this before? (The only difference being that he cares about his Pokemon. Gary was all strength and crap.)
Basically, they just reused the formula with Gary and Ash, but then, in my opinion, I don't think this rivalry works AT ALL. Trip is a beginner trainer, and Ash had already gone through so much throughout the series. Our first rivalry with Gary and Ash worked because they were new trainers, and Paul and Ash were on equal grounds. Ash should be owning this sucker, not the other way around. :C
tl;dr
Appearance-wise: Trip = Paul;
Character-wise: Trip = sort-of Gary (before he became less of a jerk xD);
Rivalry-wise: Trip VS Ash = Gary VS Ash
