First of all the good, #Music looks great on iPhone and does indeed allow you to play music through the app if you are a Spotify or Rdio subscriber (if not you'll get the 30s iTunes preview of each track).
From there on in though it all starts to look a little woolly.
Whereas products like last.fm mine huge amounts of data produced by users scrobbling their listening activity to work out the relationships between different artists, Twitter's service bases their recommendations on who you follow in Twitter.
Don't follow any bands? You aren't going to find much value here.
Even if you do follow some artists, basing recommendations for music listening on who they are following just doesn't seem like its going to work very well.
For Twitter its a potential gold mine, if they can push users into buying new tracks from the iTunes music store (on iOS anyway, presumably the Play store will replace this on the Android client) their tiny cut of the proceeds could amount to a significant chunk of cash if popular. Artists too will be hoping that this supplants streaming services for the greater returns they get. Expect lots of talk about the service from those most likely to benefit.
However if you're really looking to find new music that's been properly matched to your current tastes, I'd strongly suggest installing a scrobbler and getting into Last.fm. Cloudscrob for iPhone or iPad; or the official Last.fm Android app both work well, as does the desktop plug-in for iPod users. In any case, once the service has had a chance to parse your listening you'll soon find yourself getting relevant, useful recommendations.
Your ears will thank you for it.