It depends on the bass and on you, you have to try a few out before you'll find one that kind of 'suits' you. Once I found my 'brand' so to speak I adjusted very quickly, well, instantly really.
Neck dive isn't inevitable, only one of the eight or so short scales I've played had neck dive, mind you, they have all had lightweight tuners. If you are moving from a P bass then I completely agree with @Lozz196, Mustangs are the way to go. I also had a JMJ and it was glorious, I never noticed any neck dive but, again like Lozz, I have straps that provide good support.