As with any prescription medication, there shouldn’t be a huge difference between a brand-name pill and the generic kind. Lots of times insurance plans will only cover the generic, and they’re less expensive if you don’t have coverage.
Some companies that make birth control pills will give you a card that you can give to the pharmacy wherein the company will actually pay the difference in cost for you so that you can get their product - Alesse and Marvelon are two examples of companies that will do this; check their websites.
Also worth noting is that if you switch pills anytime, whether it be from brand name to generic or to a different pill altogether, it really is a good idea to wait a month before you rely on it for protection against pregnancy. The different hormones may affect your body differently and it’s possible you could ovulate, so use an additional method of birth control, such as a condom, in the meantime.