A live gig is just as much of a snapshot as a recording. (Unless you're attending every single gig someone plays...)

Someone mentioned the signature sounds of certain producers that render their albums immediately identifiable (Phil Spector, Brian Wilson et al). But even relatively unadorned, stripped-down albums often have a signature sound too.

I'm listening to some 60s Lightnin Hopkins recordings right now, and even though it's just the man and his guitar, there's a lovely reedy degree of distortion on his voice, with a tiny bit of boxy reverb on it too, and the guitar is panned to an extreme. I love the production on Shirley Collins' 60s recordings too – the shrill reverb on her voice, the way the unusual instrumentation is so carefully placed (think Death and the Maiden, for instance).

Studio recordings can be really characterful and interesting in very subtle ways – even when it's "just" a folk musician using the exact same set-up she always uses.

These days it's the opposite problem most of the time: studio recordings of folk musicians are far too overproduced and polite. Good recent case in point would be Nancy Elizabeth Cunliffe. See her live and it's just her, accompanying her singing with either a harp or a guitar. Beautiful stuff. But her album's just a completely different artist basically and I find it unlistenable: fussy instrumentation, double-tracked vocals, tokenistic arrangements and overdubs, overdubs, overdubs. Trying far too hard to be clever. I really don't understand why when so many musicians get in the studio they immediately proceed to ignore everything that got them there in the first place.