Both Spotify and Pandora offer a free version which is essentially a very basic form of the pay service. The Pandora service offers unlimited listening with commercial breaks every three songs. This is similar to a typical radio station (except with a few more commercials) with the ability to skip up to 12 songs every 24 hours. Spotify only allows free users to listen to 10 hours of music, also with advertising, and you won't be able to listen to any one track more than 5 times.
The pay service is where the competition gets interesting. Pandora offers a single plan that costs $36.00 per year. The Pandora service offers higher quality audio tracks and the ability to skip tracks more often. They also eliminate the commercials. So, for $3, you get your music streamed to your computer, phone, tablet or car without any commercials.
Spotify offers two plans, both more expensive than the Pandora for a year. The first plan, Spotify Unlimited, costs $4.99 a month and allows a user to download music to a specific computer without any commercials. The Premium plan ($9.99 a month) allows unlimited downloads to any platform (computer, phone, tablet, car, etc.), and adds offline access to your music. Spotify also offers early album launches with this service.