If the "sound quality" is moved closer towards reproducing the performance, then it's "better" by anyone's book. If you prefer to modify the sound to suit your preferences, then it's "different" - and "better" to some but not to others.
In general, the "live performance" (having seen a few - and participated in a few) - is rarely - almost never - as good as it is in my living room. Sure, the "ambiance" and so forth is unrivaled, but I could say that for a Larry the Cable Guy CD too. The balance, the mix, the artist's intentions - these are usually better in my living room.
Live performances are full of "soft" edges from echo, errors by performers, gear that malfunctions, and people that scream over my favorite parts. NOTHING is like a live performance, no doubt. But it doesn't usually sound "better" if you define "better" as "closer to what the songwriter hoped you'd hear."
Having said all that - if the recording sucks, then, yeah, I wanna hear it that way. Anything else is cheating!
