From my perspective, there are no hard and fast rules governing a live recording. For example, my favourite live album is Renaissance's "Carnegie Hall", which I prefer to all their studio albums. That's not to say I don't like the latter - on the contrary, I love all of them from 1972-77. It is beautifully recorded and sounds fantastic. Conversely, my favourite Grand Funk album is the "Live Album" and that is a sonic train-crash, albeit an exiting one!
I suppose it helps if your brain (and ears) are attuned to the dynamics and soundstage of the concert hall. A recording made on the stage will sound vastly different to that of one made in a studio. There will be differences in tonal quality and of soundstage and quite likely some factors that would otherwise be deemed intrusive - building characteristics and audience participation notwithstanding. A lot of those factors will be seen as a positive boon to those that love the concept of the live recording and studio made performances may be seem stilted and contrived. Of course one needs a system that will reproduce, to the listeners satisfaction, and as far as is possible, the sonic signature of the concert hall.
Personally I like a balance, both of studio and live but also of the different sonic characteristics that are presented. I love both the excitement and immediacy of a live recording just as much as a beautifully crafted studio recording.
