Is the CIJ jazz better? - ignore amplified tone for the moment.... better feel, respone, playability, weight, whatever, is it berrer?
If it is, swap all electrics (pickups, pots etc) over. If not, move on.
Beware the 'new bass' efffect. I have too many basses, currently on big hit with cheapy basses (Warwick, chinese, £130, shagged strings), they sound great. 3 months time, my G&L back to the fore.