I think a lot of it boils down to energy and gravitas. I remember going to an HFStival in DC where Godsmack was headlining. Now, I'm not a fan of theirs in general (though they do have a few decent songs) but my wife, who dabbled in Wicca, is all about them since their a Wiccan band. Went through the day, saw a bunch of local and mainstream bands, (and ran for the hills when Good Charlotte came on), but then AFI came on. I'd always liked their music, but I'll be damned if their live performance wasn't one of the more amazing shows I'd ever seen. It was just plain rocking out and they nailed it. Then Godsmack comes on later that evening with shitloads of pyrotechnics and girls in bikinis and light shows and fog machines and all sorts of props, and I couldn't have been more bored.
Bottom line, as long as the band really draws you in then I couldn't care less about how similar or disimilar they are to the studio work.