Maybe the game is able to detect the mod-chip inside the psone, but not inside the psx console.
For the psone it's much more difficult to provide a real stealth funcitonality. So the most modchips that are sold don't provide a shelter against modchip detection for the psone.

I assume that there are different ways to detect a modchip out of an application.
So even if you use a crack/patch, you can't be sure that it works 100% with every configuration (ps-type / modchip-type).