I like both, though it really depends what sort of music it is. Some stuff doesn't sound as good live for instance the Haxan Cloak, live is cool but it doesn't quite convey the atmosphere of the music as well as it does in a clean studio version. On the other hand though some artists sound just as good live as in their albums, Jason Molina is one that comes to mind:
Depends on the type of music.
A lot of old classic shit that I love like Johnny Cash, Bob Dylan, Donovan, The Eagles, Rolling Stones, Boston, lynyrd skynyrd etc etc like classic rock, soft rock is great by my standards to be played live. I even prefer some songs to be live when I listen to them.
Other genres like rap, to me, shouldn't be enjoyed live (on your iPod or whatever) if you're going to the live event then that's cool but I personally cannot stand rap/hip-hop live (most of the time) when they do TV events (tonight show and such) they will go all out and look pretty good but I probably won't listen to it more than once.