Rhapsody costs $10 per month and Pandora is Free
Rhapsody has a few million subscribers and Pandora has 50M plus users
Pandora has advertising and I assume Rhapsody does not
Rhapsody has 8M songs on its playlist which is larger than Pandora
Pandora customizes songs you might like based on other bands and songs
Rhapsody allows you to stream just about any song or album
If you don't care about owning music and just want to listen Pandora is better
Rhapsody is a spin-out of Real Networks & Pandora is a VC back startup
Pandora is a human genome product looking for relationships
Rhapsody is a very simple subscription based streaming service
Both have Android, iPhone & Blackberry applications