The only other aspect of a "live" demo might be that if you have a recording of an actual gig and your act features stunningly witty introductions that have the audience helpless with laughter or you get obviously wildly enthusiastic applause this gives a feel for your live performance that may not come across in a studio or home recording.

With that exception I'll go along with the majority opinion of "send them the best you've got".

I've just finished cutting an album as part of a duo and while there are some heavily multitracked songs and tunes much of it is as performed live, so I shouldn't have trouble picking credible demo tracks from it. Fortunately, though it's for a label (Wild Goose), I have permission to make demo CDs from it as long as I include the necessary phonographic copyright notices.

Anahata