Spotify is brilliant. I set up a playlist of 10 songs that I liked that were kinda-sorta related. Their genres ranged a bit, but they all had a similar "feeling". I hit Play, and enjoyed the music. After the 10th song, another song played... and I liked it. Then another song. And I liked that one, too. And another. THIS is the magic of Spotify. Pandora simply randomly throws in a different song every 5th track. There's no logic to it. If you are listening to "Rock", and the 4th song plays on Pandora, the 5th song will be in the "Rock" category, but may not be at all musically related to your playlist. Spotify knows the soul of the track you are listening to, and is VERY good at finding another track that fits in the same vein. tl;dr: Spotify introduces me to new artists. Pandora plays radio-friendly shit I don't want to hear again. Pay for it. You will be very happy. (But the Spotify interface is TERRIBLE. Just... the absolute worst melange of weirdly inexplicable functions and features... nothing is where you would expect it to be, and none of the buttons or links go to where you think they will go. It's terrible. But the algorithms are SO GOOD, it is worth it.)
My gripe with Pandora is that it’s exceptionally good at finding music that has many technical similarities to what I like while managing to completely not be something I’d actually like. The “music genome” is a noble idea and all, but it really highlights the superficialities of their methods in qualifying music. I’d venture a guess that connecting bands solely by the scene and social connections they came from is a way better predictor of musical tastes than musical qualities.