1. Spotify has a slightly larger selection (8.5mm tracks on Rdio, 13mm on Spotify)
2. Rdio has a killer web app so you can login to your account from any computer (great for parties and traveling). Both have desktop and mobile apps.
3. Spotify has higher bitrate (320) on pro accounts and uses p2p and other tech to do things like pre-cache songs it thinks you're going to listen to so they play instantly when you click on them
4. I haven't used spotify much, but Rdio's social features seem more fluid and their collaborative playlist feature is awesome
Spotify is also a music management app like iTunes. So you can use Spotify to play your own music files along with their vast catalogue. With Rdio you can only play Rdio songs and if some song isn't on there you'll have to whip out iTunes or another media player.
