I never understood folks who, after hearing a live album or show, exclaim "That was great! The songs sounded EXACTLY like they do on the album!"
For me, I would prefer if a band's live performances do NOT come off as note-for-note replications of the original studio recordings. A good live recording should bring a different perspective, for example emphasizing a bassline or drum pattern that might've gotten obscured in the studio mix. Or an adventurous guitarist who will put a different accent on his solo or riff. All coming from how a player might feel on a particular day, thereby lending a totally different atmosphere to an otherwise familiar song.
I especially love bands that "deconstruct" a song, taking it apart into pieces in a live setting and then putting it back together again. Taking an instrumental section and extending it out... toying with the guitar riff, or changing up the rhythm midstream, or inverting the bassline, or even all of the above. Even if the playing goes nowhere, I'd much prefer a failed experiment than no experiment at all. When a band does this, you can almost see the creative process happening right before you.
I was listening to Zep's Dazed and Confused on a 1975 bootleg tape when, during the instrumental, Page breaks out into a familiar riff. I'm thinking, where do I know this? It turned out to be an embryonic version of Achilles Last Stand that Page had been working on a year before they recorded it for Presence. Plant hadn't even written lyrics for it and was just ad libbing some nonsense to it, which was actually quite cool. Bands like Zep, Deep Purple and King Crimson did this all the time.
Maybe it's just the prog-snob in me versus a kind of "pop" music mentality, but for some reason, many fans feel that the "holy grail" of being able to perform live is to get a perfect reproduction of how they originally heard the songs on the studio album, sound-wise AND playing-wise. To me, it just defeats the purpose.