I find the best Fender jazz basses are the new ones, built in the old style! Take my Fender Jaco Pastorius fretless. Superb construction, excellent playability and awesome tone, all from a 'new' Fender built to the old design. The thing with newer Fenders (at least the high end ones) is that they have a consistency lacking in the older ones.
Take some 70's jazz basses, for example. Some sound fantastic and are a reasonable weight, but some sound cack and some of the ash bodied ones can weigh a tonne.