Think of it this way:
Last.FM: Enter a band name and you will get a list of bands based on other bands that other Last.FM users like that also like the band you entered. Therefore potentially completely random and potentially useless. I know people how like mostly european metal, but also like Aqua and the Backstreet Boys. So if I enter Aqua I could get metal and if I enter Hammerfall I could get Aqua.
Pandora: Enter a band name and you will get a list of bands that "are similar to" the band you entered. This has the problem of the fact many bands sound very different throughout their career. Entering Mr Bungle or Faith No More or even Smashing Pumpkins could proove very strange. Heck, enter David Bowie and see what you get.
I think Pandora is more successful for me because I can think of a band that has a similar style throughout their career (like Dream Theater) and have a good idea what type of music will come out the other end.
I know how to control it. I can think "I want to hear a new prog metal band" and seed it so that's what I get.
Last.FM is, in my mind, completely random as people's tastes are completely random. If I enter a band I could really get anything. The seed is meaningless. That is of course what many people want. Random suggestions from the full range of musical styles. That is a nice alternative to radio (which tends to force the latest hit down your throat, repeats, and you can't skip).
Use them both. Be aware of what they both do.
Pandora would benefit hugely if you could seed to the song level. So instead of entering Faith No More you could enter "Anne's Song" or "Caffeine" or "RV" and get three very different lists of songs.
I might also add that entering "Faith No More" into Last.FM brought back a list of bands and CDs that described almost my whole CD collection from the 90s. So in that respect it did a brilliant job. It predicted my music taste very well. But it didn't recommend a single thing I hadn't already heard. Pandora, not being based on taste, is more likely to bring back obscure artists in my mind.
Q: Where does Celery come from?
If we just gave our testers access to the internet we wouldn't have this problem now would we...