I went to GC the other day and played a CV Jazz and 50's P, and I gotta say, I was disappointed with the P. My GAS died quickly.
The frets are so tiny on these CVs! But they were done right, no sharp edges. The neck on the 50s P was a little too sticky for me, I found I couldn't slide down the neck like I do on my MIM Jazz. Sound wise, it was alright. I think I prefer split pickup P's instead of SCPBs. But the noise was unbearable. I've seen pics of these CVs taken apart and they have a very nice coat of shield paint in the cavities. I guess its either the inherent design of the single coil, or it was the the room i was playing in. Finish wise, the paint was a little rough around the input jack, but other than that, perfect. And it was super light, to me at least. Regular P players might find the weight normal.
As for the CV Jazz... I think I got another case of GAS!

The neck was perfect, not as sticky as the P, and I love a Jazz in white/tort. The only bad thing about the one i played was that the chrome on the bridge was a little scuffed up. And the 3 ply (white-black-tort) pickguard doesnt look anywhere near as nice as the 4 ply ones Fender sells for aftermarket.
Now I just need to find a 60s P to try out.