I've been playing bass for a day or two, and I've owned/own a bass or three. I've played small, medium and large venues. I've done some studio work. Here's my naked conclusion that's sure to get me flamed:
1. Live, regardless of venue, I can accomplish just about any type of music I play (does NOT include Jazz) with just about any type of serviceable bass on the market today. Yes, I'm a recalcitrant, degenerate, unrepentant bass whore. There are a very few exceptions, but generally, through playing style, amplification, and on occasion modeling, I can get it done. I'd bet 90% of you who play at a high level might agree even if you don't want to.
2. In a studio setting, this is, generally, not true.
3. Yes, certain basses feel better (completely subjective, mind you...) and for a long time I'd never get on stage without one of "those" basses, but now it's really not that big of a deal to me. Personally. I'm going to rock it, or not, based on ME, if I've communicated will with my tech and sound man, and...well that's it.
4. Excuse me now while I go scour the TB classifieds and evil bay.
5. As one poster stated, the P-bass may well be a one trick pony. Though I'm no Fender fan boy, I'll admit that on trick is a HUGE portion of the genres most of us play. And if you're headed to the studio for payed session work, you can bring all of your fancy favorites with you, but 30 minutes in, you ARE going to be plucking or picking away on a P-bass. Bet that. I think that's why most of my newest custom builds are passive.