Zero dollars flow to music license holders via Grooveshark. It operates in a legal grey area. Also the file metadata is set up by uploaders and is a lower quality than Spotify in most cases. I don't know what the Grooveshark Android/iPhone client is like, but Spotify's is decent.
Grooveshark isn't really legal, otherwise they wouldn't be being taken to court by just about any record companies. By using Spotify you're really rewarding the artists you listen to.