Spotify is 100% licensed. AFAIK, Grooveshark is more like Napster in that it's a free-for-all with user uploaded content, though they have worked out deals with some of the record companies.
As far as I know, barely anyone use Grooveshark in Sweden while practically all my (University) friends use Spotify. Doesn't Grooveshark have some quite dodgy habits when it comes to paying the artists/using legit music files? Or was that some other music streaming service?
If nothing else Spotify has received a lot of good press in Sweden simply because it is Swedish. Patriotism :) And this was a Swedish study after all.