I've heard some of their live stuff and it seems that they somewhat kept the tune of the album recording but seem more interested in jamming on stage. Is that an accurate representation?
It's a more positive way to look at it, but probably not inaccurate - except I'd be more critical of "somewhat kept the tune."
They seem to consistently make excellent studio music - and that doesn't always translate well into live performances, to be charitable.
http://www.guitaralliance.com/ROMTOP100/songs/she_talks_to_angels/black_crowes_the-she_talks_to_a.pdf
They're very, very difficult to cover live. I do not actually recommend going to see them perform live - they pretty much suck live. They're one of those bands that should have stayed in the studio.
Why?
'Cause they make great music.
The issue is that they use a never-ending series of alternate tunings and they incorporate sounds that are difficult to replicate in a live environment. Their music is (often) musically complex. It's fucking brilliant - and I generally think an alternate tuning is a moronic idea.
Seriously, they suck when live. Horrible... Absolutely horrible. They are also kinda assholes, but I'm a bit doubtful that you're interested in my airing dirty laundry.