It depends on the music. Acoustic music (classical, for example) was developed around acoustic performances, and performers fashion a sound that works "out front" versus at the output point of the instrument. The acoustics of the room become part of the performance, quite intentionally. One symphony tuba player I know selected his instrument specifically because it worked in his orchestra's performance space. So, I don't want a dry performance of orchestra or large chamber music--I want to hear as much of the performance venue as was originally accommodated by the musicians.
Of course, audiences for such music generally at least try to keep their own noise down. For me, that upsets live classical performances more than anything--the noise made by other patrons.
Acoustic jazz needs a small venue, because the musicians craft their sound for a small venue, and with amplification writ small, so that it doesn't sound amplified. My favorite live jazz experience was hearing Maynard Ferguson at the 200-seat La Bastille club in Houston back in the 70's. But I also listened to Jim Cullum at The Landing in San Antonio, which was even smaller.
Just last year, I attended a concert by Rick Wakeman, playing piano and electronic keyboards. The venue was the good-sounding and fairly small Birchmere in Alexandria, VA. And everything was clear as a bell, except for the mid-range of the piano, which was boomy to the point of muddy distraction. That could easily have been avoided, in my view.
For rock music, however, the concert isn't for the listening, it's for the experience of seeing the group in person. I've never heard massively amplified rock music in a large venue that sounded as good as a studio recording.
I attend bluegrass festivals from time to time, and those are usually outdoors. Usually sound quite good even amplified. But orchestra concerts outdoors, even with amplification? Uh, no, unless there is a really effective shell around the stage. And when my quintet gets booked for an outdoor performance, I cringe--every mistake and imperfection suddenly becomes dominant, and I feel like I have to increase my volume four-fold (with really unhappy consequences).
So, it really depends on what the musician is trying to craft--orchestra musicians are specifically crafting sounds that work in a somewhat reverberant venue, while pop stars who optimize for their recordings are crafting sounds that work best in a dead studio environment. Studio recordings from them are always better acoustically than live concert recordings in my experience.
A special case is Philip Glass's ensemble, which is a mix of acoustic and electronic instruments, amplified very loudly. I heard them in a 700-seat auditorium at Southwestern University, which was life-changing, and at the 3000-seat University of Texas Performing Arts Center, which was flat by comparison. Their sound mixer sits on stage and is considered one of the performers.
I've also heard (for example) the Canadian Brass at everything from a 900-seat dead, deader, deadest high-school auditorium to an acoustically live 3000-seat concert hall, and they always sounded excellent with no amplification. But, again, the instruments were designed for interior spaces of varying resonance.
Rick "context is everything" Denney