If I played my Hofner the way I played my pbass, the bridge would have shot across the room and blown a hole in the wall. Each instrument has its own characteristics- so yes, I think there is a difference. With that said, you can play any kind of music with any kind of bass.
All I’m saying is there are differences but not limitations although some adjustments have to be made.
just another opinion
this, exactly this. every guitar - acoustic or electric - doesn't sound the same or have the same amount of sustain nor does every violin, piano or anything else with wood and strings. i have 2 small harps, and they sound completely different. one has much more sustain, but my favorite of the two has much less sustain and lower notes. i love it.
there's no reason the gibson should sound the same as the P bass, and there's no reason to play it differently to try and make it sound the same. and you can still play the same songs with both, with each bass adding a slightly different flavor to the songs.
btw, for some of what i play on bass, i actually prefer less sustain.