Spotify and last.fm aren't even that similar.
What sets last.fm apart is the great community effort and recommendation engine. I use it all the time to find and - actually - BUY new music as well as finding out about events that I might otherwise have missed.
Spotify is great when you already know what you want to listen to but I find the music discovery factor of Spotify to be sorely lacking.
Can't wait 'til Spotify provides an open API and someone provides a nice mashup to stream my last.fm recommendations through Spotify!
(I've seen some hacks based on Spotifys Google Docs spreadsheets providing parts of this functionality already.)
As it stands, EUR 3 for last.fm recommendations and free radio streaming is just "OK". Spotifys EUR 10 for on-demand streaming is also just "OK".
I'd pay last.fm EUR 10 a month in a heartbeat if they'd combine their recommendation with Spotifys ad free on-demand streaming.
A partnership brewing, perhaps?