I think the difference is that "disculpe" is more polite than "perdón" or more impersonal, a concept like the difference between "tú" and "Usted", and the two ways to apologize have the same valuer.

Perdón you can use in little situations, like letting something fall, or bumping someone by accident. You can also use "perdóname". Disculpe can be used in the same situations. There's no difference, but the most used is 'perdón'. 

 Perdón is like "apology" and they use as sorry. And disculpe is the true sorry, but they don't use as much they do to the other.

 In more serious situations, you can say "lo siento" as "i'm truly sorry". To express regret there's other expression also: "lo lamento".