I'm not sure piezo pickups are the place to look for "air", but that said, the J-Tone Big pickups do have quite a thick, midrangey tone that can come across as a little electric - it's perfectly usable, but you may find you like others better. And a lot of players find they prefer a single element pickup to one with two sides - I would try the J-Tone with one element hanging loose first just to determine if that's a good direction to head in.
I'm getting results I'm quite happy with using the KNA DB-1. As pickup sound goes, it's fine, and the high end is more open sounding than I got with a single element J-Tone on the same bass. But both the fit and the way a pickup responds on your specific bass can be extremely variable, so don't take that as a firm recommendation!