I have been using both of these online music streaming sites for some time now and really finding it hard to decide which one I should stick with. They are both really good services. Last.fm is totally free, however you can only create a radio station to listen to and it will stream all types of tracks related to your artist search. Spotify has two services, the Free service that has Ads every now and then and the premium service which is £9.99 a month I believe that contains no ads.
Quality wise, through cheap ish head phones there is no real difference in the quality of either service, however when I played through my home cinema (which is about 9 years old now) and not very high spec I could hear the quality difference, Last.fm seemed to be that bit clearer than Spotify.
Last.fm has the added advantage that you can play it through your web browser not just through the client that you can install on your OS, where as Spotify you need to install an agent on wither Windows or MAC, also Last.fm has a player for the iPod Touch and iPhone.
Over all for my use I think that I will stick with them both.
www.last.fm
www.spotify.com