Yeah I use both services as grooveshark have some songs that spotify misses and vice-versa. Spotify is also a standalone program, so it doesn't eat a huge amount of ram that the web-browser need. I do also find spotify easier to manage and use.
for those that doesn't know what the program is, it's a simple music player that Audio streams in the Vorbis format at q5 (approx ~160 kbit/s), or optional q9 (approx ~320kbit/s) for Premium subscribers, the highest streaming rate for any online service.
You can also connect it with your facebook account making your choice of music available for your friends.
If you choose to pay a monthly fee you will also get rid of commercials and can "download" the songs to be played in offline mode. You can as well get spotify in your iphone/ipad and andriod phones. There are more cellphones that can use spotify as well. I know Some Nokias can do it.