The downside of the Model Js is the lack of high end (which may not be a big deal for your based on the adjectives you're looking for). To me, with the Model J bridge pickup soloed, it still sounds like a Jazz bass, but with more low end and less high end, and plenty of midrange. With the Model J neck pickup soloed, to my ears, the bass no longer sounds like a Jazz bass. It's a bit too boomy and muffled. Right now, I've got the model J in the bridge, and an Area J in the neck position. It's a nice combination. The Area J sounds great — a bit fuller than the original pickup, but with nearly all the high end of the original, and one of the lack of definition of the Model J. Despite the fact that it's a humbucker, it sounds really close to a single coil.
I'll probably try an Area J in the bridge (because I wouldn't mind just a little more high end), but the Model J really does sound great (and the other bonus is that the Area J and Model J are totally silent).