The desktop UI is clunky and cluttered with several calls to action on the main 'player' screen - they cram everything in into one view and it's not clear where to begin. Meanwhile the mobile UI is pleasant, simple and provides only the major functionality on the main screen. It is a minimalist design with very few buttons and choices for the user to make; other less-frequently used functionality is deeper in the application.
Whether this design is intentional or due to the natural constraints of a small screen, it works. Not only is the desktop design less pleasing, the inconsistency in the look and feel (across channels) makes it difficult to learn the overall Slacker model. They should strongly consider a more consistent design across channels! In addtion to simplifying the desktop UI, another improvement could be a small, simple app (similar to mobile) available from the web browser - like Pandora One.
Overall, when building music applications in different channels, designers should look first to small screens as inspiration. The simple design of mobile applications (like Slacker) can help them translate to a great user experience on a larger screen.
Update: Evolver.fm has written about a new Slacker mobile UI here...http://evolver.fm/2010/10/27/slacker-app-pandora-spotify-iphone-android-blackberry/#more-364.