I am partial to last.fm because of the extensive collection of international music it has... Pandora doesn't seem to encompass as much music as far as the international scope goes.
Then there's the matter of having a nice little last.fm extension for Firefox that plays all my favorite music as soon as it loads up =D
When Pandora was in open beta and available worldwide, I used it some and got to like it. Especially because the music they suggest you really is of your taste..
Real pity they made it US only!!
Whereas Last.fm is loaded with... lots and lots of stuff.. which I think is somewhat superfluous. Not to note that their interface is somewhat lacking, not really userfriendly. However it is free, has much more music than pandora and works worldwide.
I don't think I can really decide for which one to vote.. Thus, I won't vote! Not until something changes...
I use pandora more the ipod touch app is so nice when you want to listen to some other music that you don't have on the ipod. It can give you really nice stuff to listen to too. But i haven't used much of last.fm though.
I've been using Last.fm for about three months and I absolutely love it. The recommendations it gives me are spot on. I've only experienced a few problems with scrobbling issues (that is, tracking the songs you play), but the staff were extremely friendly and efficient. Awhile ago I used Pandora, but I didn't find it as useful as Last.fm. Last.fm is easier to navigate, gives better results, and just looks better.
I used to use last.fm a lot and it was rather good, but the ability to choose what songs to play annoyed me a bit. As a direct result I now use Deezer, which allows you to stream whole albums unlimited times for free. The only disadvantage is that a lot of the site is in French.
Out of the two in the poll though, I would personally go with last.fm.