This is a timeless argument (because 3 years is timeless) that has led to many fights. I decided why don't I tackle this debate and so I did my research and I present you with this:
To The Eyes
If we are comparing how they look it is like comparing socks to bracelets. Spotify's free service comes as a desktop app while Pandora is free when accessed online Spotify looks more like iTunes and has lots of information. Pandora is said to look "washed out". Spotify also has the advantage of adjusting screen size whereas with Pandora it messes up your whole screen.
Spotify wins this round in terms of a nice, well-organized screen.
Inventory
(based on numbers that both music services self-report) Pandora has a catalog of over 800,000 songs. Spotify has over 20 million and they add 20,000 everyday.
Spotify blows Pandora out of the water.
Social features
Pandora lets users connect via Facebook (only American friends). Spotify offers Facebook, Twitter, and Windows Live Messenger connection. You can connect with other Spotify users and Pandora now allows that option as well. (Spotify is more global and you are able to connect with 28 countries).
Spotify wins the social network options. (If you are a social person, great!)
Free Version Restrictions
listening to music for free does mean you have to deal with ads =( Both apps have annoying and repetitive commercials. Pandora has them about every 5 or 6 songs. Spotify ads on the other hand are not as frequent, but they will ruin your jamming experience and stop the app for 10 minutes. Pandora limits the amount of times you can skip songs on a station. Spotify limits the number of hours you can listen to for a month to 20 hours.
That is horrific that someone would try to cut you down to 20 hours a month. Therefore Pandora is the winner.
Paid Features
Both offer a paid version so you do not have to listen to the ads. Pandora One has better audio quality, ability to skip more tracks and is only 6$ a month. For Spotify you could get their unlimited plan that eliminates ads, unrestricted access to music, and cost you 4.99$ a month. Or you could buy their premium plan fort 9.99$ a month, get everything from unlimited, have a music catalog on mobile device/tablet, and listen to playlist music while offline.
Pandora wins this one because of their amazing price and the updates to Spotify will not be beneficial unless you specifically plan to use it every day.
Conclusion
It all depends on how you plan to use it. I know I'm sorry if you came here thinking you would find out the biggest question in the music world. If you want to discover new music go Pandora and if you are only looking to get rid of ads, go Pandora. More interested in connecting with friends and creating a playlist: Spotify. Personally I use Pandora on my phone but if I were to be on my computer more I would go with Spotify.