I don't want to step on anyone's toes but I really feel that no matter what style you are playing there are certain standards to good trumpet playing.
Some of your concerns about the differnce between jazz and classical playing is addressed in equipment trends. Since jazz players tend to play more intense(high, fast, loud) music for longer periods of time they tend to play mouthpieces that are a little smaller and sometimes trumpets that are a little lighter in weight and perhaps more resistant.
I don't think that the approach to the instrument itself is any different. Tonguing and sound concept may be different you must still have a clear tone, strong technique, good range, the ability to play loud and soft, and the ability to change styles. I think about how to approah Ellington, Clifford, Metheny, Kern, and Jobim as much as I think about how to approach Haydn, Bach, Gabrielli, Bartok, Berlioz, and Arban[played 'em all
].
Manny, as a jazz player I do spend a lot of time learning tunes and scales, and chords but I also keep up with my Arbans, Charlier, etc. because while I'm working on my jazz playing I still have to work on my trumpet playing. All my teachers who have been jazz players practice etudes and classical solos as well as jazz playing.