I feel as though Pumped up is the more "complete" character of the two.
If you really favor strong rushdown and place less value on zoning, then Wrestler is your man with that command grab.
However, Jax already has insanely good buttons, as has been previously stated. Energy Wave, Ground Pound, Air Ground Pound, and Instant Air Ground Pound all work together to provide a highly atypical, but also incredibly powerful, zoning kit for Pumped Up Jax.
Some zoning tips: Alternate between Energy Wave and Ground Pound in order to mix up your opponent. Energy Wave effectively anti-airs most jump ins, while Ground Pound catches people attempting to neutral duck your energy wave.
Additionally, you can get (what I believe to be) a guaranteed additional 13% OTG if you use Ex GP after anti-airing with your energy wave. Other guaranteed or near guaranteed OTG setups include Downward Dash Punch, b121, f212, anti-air d2, and 111 on juggled or airborne opponents.
While the startup frames of Ground Pound are slower (36 frames) than those of Air Ground Pound (25), Ground Pound has an incredible 21 recovery frames. Oftentimes opponents who jump my GP and overzealously run in for what they are sure will be a punish end up eating my raw EX Super Gotcha for 22% and a +3 restand.
Meanwhile, Air GP is Kenshi level punishable at a ludocrous 44 recovery frames. That, and GP low profiles a great deal of the game's mid projectiles; Air GP does not. I suggest using Air GP, including the Instant Air, sparingly. Your mileage may vary.