The Soloist, predecessor to the Jazz, was a straight .470 bore trumpet, with a standard tuning slide. The Jazz model, with the "expandabore" design has a reversed-leadpipe. Most of the early Jazz models that I've played were fairly open... however, they may been "Callet-ized".
When Jerry started doing the 3rd Valve Conversion (á la Pre-War French Besson), it gave the newer models improved response, and slotting. I believe that was just prior to 2000. Around that time, Kanstul had updated their tooling, and the horns had tighter tolerances, improving the horn even further.
Back on the leadpipe track, I think that you can see from the pictures below, the differences in appearance between the Superchops and Jazz models.
As you can see, the Jazz resembles a Selmer "Balanced" model, in the placement of its valve block. More than likely, this design had a great deal to do with Jerry's affinity for the playing-style of Harry James.
Also visible, in the picture, is the heavier receiver used on the Superchops model. The bell of the Superchops, as mentioned in a previous thread, was based upon the Mazereau bell. (The Mazereau company had actually made many of the bells for the Pre-War French Besson.) The Superchops bell was made of heavier gauge yellow brass, and required a heavier reciever, coupled with an efficient leadpipe, to provide resonant energy to the bell.
Best always,
Bruce