Thanks, Dr.Mark and Happy New Year to all!
The primary difference between Classical and Jazz, as I see it, is in ear training. I am amazed that jazz musicians can play by ear, or tell if a chord has a #11 or a b5, yet I think nothing of sitting in an orchestra and "throwing my ears" 30 feet or so to tune a unison note while maintaining intonation in the section, lowering a tone by 14 cents because it is the third of a chord and reading anything put before me the first time. (That doesn't mean I can play it, but I can read it.)
It is rare to find players that can improvise and play head charts and play Classical literature with attention to detail, sound and style.
One thing these players have in common is time spent in the Arban book.