Aerodyne (IIRC) has the P-pup placed slightly higher than the usual sweet spot. Mellows out all the strings if soloed. Just think of a Geddy Lee when thinking about the 70s jazz. I'm guessing you're referring to the MIM RI which I'm not sure if they share the same pups as the Geddy, but you really can't go wrong with either. Just remember that you get that extra spank with the 70s jazz due to the pup placement (and it completely covers with a bridge cover) while you get the punch of a P-bass with the Aerodyne. If weight is a concern, go with the Aerodyne. If not, the 70s Jazz is just as good.
Edit: FWIW, you can also try saving up slightly more ($750 to be safe) and purchase an official MIJ Aerodyne (not a MIJ made for US one) that has a pickguard, different color options available, and traditional jazz control plate (not that football strat jack). http://store.ishibashi.co.jp/ec/pro/disp/1/05-321098900
Really nice basses and Ishibashi Music has a good rep over here with many TBers purchasing from with without a problem - they also have reps that speak English as well.