Yeah it's all home-made arcades here.
To answer your question though; When namco planted the rom for PP onto the PS2 disc. they most certainly did not make adjustments between between the turning speed for a wheel, and a thumb-stick. A wheel does, work for the game, and it does work much better, the turns are still immediate but you don't slam into the sides and have a chance to correct your steering.
It's unfortunate case of bad porting.