It used to be, live albums were nothing more than louder, faster versions of the original album music, with screaming (Cheap Trick at Budokan comes to mind).
There's a new crop of live albums that I'm loving, the latest being "Live Music" by the Joe Jackson Trio.
Jazzed-up versions of classics such as "Sunday Papers" and interesting covers including the Beatles' "Girl" (which I've heard him do in concert) and Ian Dury's "Inbetweenies" (which I haven't). I've got four live Joe albums now, including "Summer in the City" and "Two Rainy Nights" plus the double live album (which is the weakest of the four). Now if we can only get him back in Chicago (he's avoiding the US for its anti-smoking laws).
Artists (at least the ones I'm buying live albums from) seem to be able to take more liberties with their own music on today's live sets. Try Glen Phillips' "Live at Largo" for some stripped-down, pure singing. Try "Katie Todd Live" for some of the best, jammin' versions of her early works (and I was there at Milwaukee Summerfest during the recording). Try "Try" by the John Mayer Trio :)