You guys aren't making it easy!
I think those that have mentioned that based on what I said in my OP, I have some biases to certain basses so let me murk that up
The Warwick I actually sold about 6 years ago and was the only instrument/bit of gear I ever regretted selling. I had the good fortune to be able to a) buy it back and b) buy it back for what I sold it for but with a way better preamp config (MEC replaced by an ACG Filter Preamp). It's got war wounds that only I can explain. It sounds great, and plays wonderfully well although I can't quite get the action low enough for my playing now. No one loves the shape but I'm used to apologising for it

In the set I like that it can cop P tones really nicely but still sits between the Jazz and the P
The P Bass has been my number one for the past 6 years - the second best I've ever played (the very best one the guy would not part with for any money). Done a lot of gigs on this one – lowest action of any bass I've played, just sounds like a quintessential P, and always works without trying. It's got mojo and although I don't have much to say about it tonally – it just sounds like a great P bass but then I tend to think the P bass formula isn't hard to get right.
The Jazz was a punt – it came up for VERY cheap locally with bad photos and what looked like neck cracking. Turned out the cracks were only lacquer deep, and was a superb playing bass. One of the few instruments I haven't mucked around with pickups or electronics – I tried an Audere Pre and Nordstrand NJ4SV's but they didn't add much so I went back to stock. Only thing I changed on the bass at all was the bridge due to the saddles spreading apart when I played.
Stingray is the newest - always adore the Stingray neck which seems the sweet spot between J and P necks. I have a more mercurial relationship with Stingray tone – some days it is impossible to imagine any tone sounding better, others it sounds like you're kicking a wet cardboard box. It's the most affected by other sounds in the mix, where the P will just do its thing. It can be magnificent or terrible. That's based on the 3 band EQ though - 2 band EQ's have always been where it's at for me.
TL;DR
Warwick – Sentimentality + Versatility
P Bass - Effortless + Mojo
Jazz - Best player + Rarity of awesome
Stingray - Best of all noise...when it's in the right mix
Right now based on replies I'm probably leaning either P bass because Warwick covers it OR Warwick goes because it's ugly and doesn't have it's own definite tonal space