I have plenty of Fender Jazz basses (MIA, MIM, MIC, CIJ) all bolt on necks, all maple necks with rosewood or PF fretboards, some active some passive.
Sound - my preference is the TBird
None, I repeat not one of my Jazz basses sound anything like my 2015 Gibson Thunderbird. They all have more honk, more nasal twang, more bark and more top end than my Bird. Conversely, my Bird has more mids and more low mids and about the same bottom end, but more punch, more grit, more growl, and more sustain than my Jazz basses.
Playability - my preference is the TBird
Both the Jazz and the TBird are comfortable to play while sitting but when standing I prefer to sling my basses down around my waist or lower and the Bird feels better there. Neither exhibits any concerning neck dive. The Bird neck feels a tad thinner and narrower so fretting hand speed feels a bit faster on the Bird. My (floating thumb technique) right hand always seems at a loss for a thumb anchor when playing the E string on the Jazz since I have a tendency to hover between the neck pup and neck. On the Bird it just naturally falls on the corner of the neck pup so it feels better in that sense. Access to the controls is just fine with either bass but after playing Gibson guitars for a while I really became addicted to the ease of quickly rolling volume or tone up or down with the speed knobs, but either bass can be equipped with those.
Feel - tie
Both basses are top notch in quality fit and finish for their price ranges. No sharp frets, no wobbly knobs or sloppy tuners. Very much a tie in this category IMHO.