I supposethat with very few exceptions there's hardly such a thing as a 'real' live album other than bootlegs. So, what's the difference, then, between a raw live album of that nature and a carefully crafted studio album that might take months, 147 overdubs, called-in musicians to cover parts, and 27 argument-filled mixes to complete?
Some great performances, full of the the artists' adrenaline, energy and kharma, inspired moments of improvisation fueled by playing to an enthusiastic audience are essentially captured live, but then touched up with varied amounts of studio overdubs and remixing.
Frankly, I don't see anything wrong with polishing great performances like that if it makes great music and great, enjoyable listening. (That said, you can't polish a turd...well, you can, but then, all you have is a polished turd.)
I appreciate the artistry at all levels of a great studio album, but some of my favorite albums to this day, that I've listened to countless times, but that I can still catch nuances of brilliance that vary from the 'original' studio recordings are:
The Allman Brothers Band's 'Live At The Fillmore East': a 'breakthrough' live album, a compilation of performances taken from a couple of different yet consecutive nights, but barely touched up with overdubs.
Bob Seger & The Silver Bullet Band's 'Nine Tonight': Seger at one point announces giddily to the crowd that they're recording 24-Track...encouraging them to be a part of the energy. Loaded with overdubs and remixing, there's stuff on this album that captures Seger and that particular incarnation of the SBB a their best, better than any of his studio album cuts of the same tunes.
Lynryd Skynrd's 'One More From The Road': as originally released, it took what the band considered their best performances from 3 consecutive nights at Atlanta's Fox Theatre. I picked up the 25th Anniversary CD version of this a couple of years ago...to hear alternate night performances of their 'biggies' (how many different versions of 'Freebird' have you found?), but also, of 'Crossroads', one of their 'honky tonk bar band' cover tunes that they never did on a 'studio' album. Here's where you hear them (at least Allen Collins and Leon Wilkeson) faithfully paying homage to one of their major influeneces, Clapton/Cream.
I'll take a great live album like those, that offer a performance I wouldn't hear otherwise, but I voted studio, if only because some artists best work just can't be captured live for one reason or another, and I'm partial to the art of great, tastefully done production with strong values, and because of the technicality that the best 'live' albums I've found were 'doctored in the studio', but for the better.