If your comparing the two like for like it is a mistake
Last.FM is a social networking site that offers music as a way of promoting artists, It allows you to find events, meet people with your musical tastes and (the most important thing) discover NEW musical tastes by comparing other peoples tastes who share similar musical tastes to your own (How Myspace should have been).
Spotify is currently a music rental application. It offers a huge range of music that you can choose from and listen to as and when you choose.
If you are looking for comparisons in terms of justifications for one over the other then as one of the previous posts states you should try to understand its like comparing a rock club to a HMV. You can listen to music in HMV, but the chances you find anything new are pretty slim. Where as in a rock club you can listen to music, but you cant listen to what you want when you want (unless the DJ/Band can play it)
Last.FM as a music lover in my opinion is a must, its brilliant for finding when artists are touring in your area and for meeting people with similar tastes.
Spotify is expensive for what is essentially mobile music on demand. The expense of purchasing the mobile client is justified comparativly to say buying individual tracks off of itunes when your standing in a train station.
Now I dont know what the costs are for running the app, but I think the marketing department were probably given to much financial reign over the apps selling price rather than actually comparing the market from an existing standpoint.
It is good to have if you have a constantly shifting taste for new music and rarely listen to your old music AND you already spend a lot of money on music, but if you dont then buy CD's from online stores and get Last.FM because if you have any lust for music then it is well worth signing up for.