If you listen to Phish or Grateful Dead, you already know live is the best.
I like live prog, but 9 times out of 10 I'm listening to the studio versions, because the nature of the music is the dynamics, and the studio offers the best environment. Same with metal, I want to hear those riffs double tracked, panned, and in superior quality.
Jazz is great both live and in studio, but in the live setting, solos can sometimes go on for a bit too long, or be excessive in technical proficiency but not have more feel, or the band meanders. Despite that, the best jazz is often live.