I recently swapped the necks of my twin P and J basses over but I've swapped them back. I'm more of a P neck kind of guy.
The P ended up being lightening quick but I found that I couldn't do big punchy feel done by the nut as well as I could before. I gained speed but lost feel on the P.
The Jazz got really heavy, and sluggish to play. It was pretty cool but I found it really lost its Jazz flavour. The pickups are Model J's so they sound more like a thunderbird than a Jazz anyway.
Swapped the necks back over and it works better. It made me want to actually accentuate the unique flavour of the Jazz actually.
I've put Model J pickups which are humbuckers with loads of low end and mids, which made it a lot closer to a P in tone. I had recently seriously contemplated getting a route under the pickguard so I could put some P pickups at the neck of the jazz, making it a convertible P/J with a new pickguard. There's already a very large route from the factory there so I couldn't have gone for the Bass of Doom look anyway.
After swapping back, I realised that what I kept trying to do was make another precision out of my Jazz, which is stupid because I already own an awesome P bass. So I decided to take out the preamp, take out the Model J's, take out the fancy series/parallel switching for each pickup and get back to the tones that make a Jazz a Jazz, and try to get away from trying to make it an almost-P bass.
TL;DR Swapped over, was interesting, swapped back.