Best example I can think of is to compare the three songs in common between "Exit Stage Left" and "Moving Pictures" by Rush. The "Live" performance is miserable by comparison.

Hmm that's kind of a poor example because Exit... Stage Left is a *horribly* produced and mastered album. I don't know if the original recording stunk as well, but something went horribly wrong in the process of getting the live recording onto a CD. There are much better live albums, including Rush's own "Different Stages."

On the other hand I *love* the versions of La Villa Strangiato and The Trees on ESL. Those weren't part of the comparison you made above, but despite the lack-luster production/recording quality, those songs make ESL worth owning.