I'll add something to what @fezz parka wrote above. "Jazz" is as broad as "rock". Rock encompasses Obituary, Foo Fighters as well as the Byrds and the Beatles. Jazz can go from Tuba Skinny to Kurt Rosenwinkel and all points in between and beyond including Bossa Nova… If you're playing trad and swing, and wanna do the 4/4 thing, you need a good acoustic archtop – no two ways about it. You might get away with a flat-top, but there's quite a few drawbacks. Same thing if you want to play chord melody in the style of the 20s and 30s masters (check out Matt Munisteri!). If you're playing electric solos in the swing and bop language, I would still argue that an archtop with a good single coil pickup (and the right amp) gets you that sound ("rich" cleans with juicy bass and articulate treble, short sustain). Listen to anything recorded by Barney in the early 50s or by the wonderful Remo Palmieri in the 40s (Dizzy Gillespie, "Groovin' High"). Not to mention Jimmy Raney, Chuck Wayne, Dick Garcia… Still, a tele might do the job admirably well – it was, after all, born for Western swing. And in the 60s most jazz player (but not Barney!) switched to humbucking-equipped archtops that were, even more than the ES-150s and ES-350s of yore, "electric guitars". For more modern styles of jazz (and I mean from Wes to today) all bets are off: it depends entirely on the sound you're going for. Mahavishnu-style fusion? A big fat Les Paul will do it… But note: archtops (especially if full hollow) still sound quite different from semis and solidbodies especially in terms of attack and decay, so it's not just the looks. We've had a long and elaborate thread on that just recently.