I can't possibly pick a favourite moment but when I saw her live these two stood out because I'd never noticed or appreciated them on the album versions.
It blew me away when she started muttering almost to herself at the the end of Cosmia.
http://www.youtube.com/watch?v=tB59Jj3Icmg#t=7m28s
When she sang the carousel line in Soft As Chalk, Neal Morgan really came back strong on the drums and everything hit home that bit harder if that makes sense. I couldn't find a clip of the show I was at so this Jimmy Fallon version in HD will have to do.
http://www.youtube.com/watch?v=DbdAVoIJ ... ed#t=4m53s