You have received very good advice already. These medications are both in the same family of medications..you have less weight gain with prozac, and that is important to a lot of people.
There are some differences in the time that they take to start working (about 28 days for prozac, about 10 days for paxil).
There are also some differences in how they are eliminated from the body (100% in the liver for prozac, 64% in the kidney and 36% in the liver for paxil).
Prozac and paxil are both ssri's. They also have a lot of similarities.
If you want to look at other information on the meds you may like to visit rxlist.com.
They're very different ssris. Prozac stays in the body much longer, making it easier to quit and generally has fewer side effects. Paxil is a very stong ssri that also strongly affects choline receptors, can be very hard to quit, and has a lot of side effects, but can be more effective for anxiety. I'd try the prozac first, in fact I'd try all the ssris first, before I'd do Paxil.