What's the difference between them?
As far as frequency is concerned
извините is used more frequently in everyday speech.
Простите is more literary and may sound pretentious. In movies it can be heard far more often than i hear it in everyday life.
As far as the meaning is concerned, my feeling is that
простите tends to be loaded with greater sense of guilt and so express deeper remorse, whereas
извините is a more formal element of polite speech, even though it's a cognate of the word
простите - means "I confirm that I did something wrong. It's my mistake. Please, forgive me." извините - means "May be, I did something wrong. But I'm sorry just for yor feelings, not for my actions."
извините are like "Ok. It's sad to be on your place, if my actions make you sad. But, generally, this is not in my responsibility zone. It's just your feelings, and I really didn't want to harm it."