Regarding neck profiles, AFAIK, there's 3 main versions of them:
THICK: the classic Stingray profile, sorta' "Precisionish", also used for the Cutlass
MED: Bongos (only ever played 2, haven't had the chance to A/B them with anything really)
WIDE: Sterlings, Caprice and Stingray5 (and some late special edition Stingray 4 string basses, I just don't recall their name).
The thin profile, my fave, is almost Ibanez SR thin (my Stingray5s are 20mm front to back @ fret 1 and under 2mm more @ fret 12), sort of Jazz shaped (a more cramped nut), but even thinner front to back than most Jazzes, except for a few, such as the Geddy Jazz, which is very close (I ignore the exact specs, but I've played old MIJ/CIJ and newer MIA Geddy Jazz basses and the old MIJ/CIJ ones felt thinner -front to back- to me, probably thinner than a 4-string Sterling too).