IME, it always depends on the type of band you're playing with and the rest of the bands mix. I love both the P and the J even though my main player is an ATK 300. The ATK fits my bands mix/sound the best. But I played with a drummer a few weeks back and he's mainly a pop/blues type of player. I brought my ATK with me and even just playing with a drummer, I could tell my ATK was too aggressive sounding (the way I have it set up) for playing with this particular drummer and for the stuff he wants/knows how to play. I'll be bringing my J bass next time we jam. Maybe even the P. I've had this exp a couple times over the years where I bring my ATK with me to play with a new project/band and find out quickly that it simply didn't fit in their mix. So I'd bring a P bass the next week and it would fit wonderfully.
So IMO, it really just depends.