@stuartk, @frogman, @tyray,
First, Lew Tabackin's flute sounded beautiful to my ear. Second, I think Andre Previn is in a very special class because he ended his career as a great conductor. I have just ordered a record of him conducting Debussy. He was also a bit of an enfant terrible, famously leaving his wife Dori (who wrote a song about him) for Mia Farrow. Although, a number of other jazz musicians are also classical musicians, Keith Jarrett, Benny Goodman, Wynton Marsalis, just to name a few.
Still I think there is a distinction. Classical musicians go through a rigorous review to be chosen for an orchestra, especially to be the lead musician. Every year they have to audition for their job, and I have seen much change over my years of watching the L.A. Phil. Jazz musicians pretty much just need to please an audience. How do I put it? They have jazz in their blood and they need enough technical precision to express that jazz.
I know jazz musicians like Coltrane were perfectionists and studied all the time, and that was one of the reasons he was one of the greatest jazz saxaphonists. And perhaps today jazz musicians need to be technically better because so many of them come from schools like Berklee where they had to audition to get in. But for just purity's sake, I think classical musicians are chosen on that basis.
Also the nature of jazz and classical musicians are very different. Jazz musicians come into their own when they find a voice. I can tell Coltrane anywhere, even if he's playing a piece I haven't heard before. Classical musicians must play Beethoven one day and Philip Glass the next. They have to adapt to whatever the conductor says they should sound like. As a classical musician, they aren't allowed to have their own voice. Although, I admit there can be a kind of swagger when they are totally into Bartok or Brahms.