While I liked rdio on my Lumia 900 it was quite buggy on the 920, but they just released v3.14 on the marketplace that adds in better WP8 support and refines the interface further. After the initial update it wasn't playing, so I did an uninstall/reinstall and now it's working very well. It no longer has skips and such when the screen goes out, and (other than my initial problem solved by an install from scratch) seems much more stable.

I listen to music all the time on my 920, so it's good to have a serious alternative to xbox music. So far the UI seems quicker, and I really like the recommendations it offers. (They improve over time as you listen to stuff). The catalog is probably a bit smaller than xbox music, but the other nice thing they have is a web client (at rdio.com) so that's a bit more flexible than xbox music. Their artist radio also seems a touch "smarter" than Smart DJ in terms of what music it includes/excludes.

The live tile can be set to full size now too (and only shows song info at full size), and if you want to be sure to always hear high quality streaming then you'll have to futz with settings, otherwise you only hear it over wifi by default.

I'm sure lots of people will still prefer Xbox Music, but if you want an alternative that has a web player and some other nice features then it may be worth giving it a try (or trying again) now that they have a WP8-friendly version released.