sooo im tied between a ernieball musicman stingray HS and a fender America jazz bass. i mainly play punk, rock, and hardcore. which is better suted for the music i play for me because i like em both.
Might as well say it...go out and play both... 2 completely different animals active vs passive, neck size, pickup config, weight, price, etc.... I have a Stingray 4H and an 08 MIA Jazz and play each for different sessions. The one thing that is for sure, you can coax a workable Jazz sound out of the HS config but you can't get the single H 'Ray sound out of your Jazz. That's why I ended up with both!
for what style you play, i would say the stingray h/s is good, but if you are really concerned about having both tones, have you look into a lakland bass with the h/s configuration, or a G&L l2000/l2500?
Dingters are known to be very elegant and IIRC they are not volunteering freely to perform punk and hardcore; that's why I proposed the Ritwall that has been known to have an affection to punk and rock
Seriously speaking, both Dingwall and Ritter play great in any style, yet from the ones the OP proposed, I think that the P will suffice
Just get something that sounds really mean, like my Guild B301 Personally, I sold off my P bass after I got a J because I never went back. I'd play the Guild more than anything if it weren't for the &!#$%@ neck dive