I understand the intimacy and emotion that live performances can evoke.
I've always liked the live stuff - if done well - take Songs in the Attic by Billy Joel, for instance - he very deliberately selected songs that have a different vibe live (as opposed to just his hits, which, like Piano Man, would have been essentially the same live as in the studio). The verion of "Captain Jack" on Songs in the Attic is one of his best, while the studio version is relatively ho hum. This is the opposite of the "intimacy", that you referenced, but the effect is the same - the interaction of artist and audience is largely implied in a studio recording and at its best, live, is palpable.
Also, take the Alice in Chains "Unplugged" album. "Nutshell" is pretty much my favorite AIC song, and I like the live version better than the studio version (and I can play it, a little, on acoustic guitar - I have an old beat up Guild D-35 that comes really close if I tune it down 1/2 step to match the record).
Other examples are live, acoustic versions of "Plush" by STP and "Diamonds and Rust" by Judas Priest, just another emotional layer is reached in those performances because of the removal of the electric guitars and a refocus on the vocals.