GC or PS2 for D-pad, 2 analogs, 6 buttons & 4 bumpers?

The game I'm interested in has a version for Gamecube & Playstation 2 which are pretty close in term of review average. My generic USB controller has a D-pad, 2 analog sticks (L & R), 6 buttons (like a turbo Sega controller) & 4 bumpers (L, R, T & B). With my PC I can play Fallout 4 at 4K with not a bad frame-rate. Which console should I go with, and which emulator for it? If it's necessary to know the game, it's XGIII: Extreme G Racing.

Thank you kindly