They are the equal synonyms. I can't agree that "извините" is more informal. You may use these both words in any companies (societies). But "простите" is a little bit less common.

"Прошу прощения"= "I'm asking for your forgiveness" the most diplomatic.

maybe извините = excuse me (sorry); простите = forgive me. btw what's the difference between sorry, excuse me, forgive me, apologize, pardon is it difficult question? ;)

извини(те) is more informal is more often in use. прости(те) is said than a person wants to apologize for a big fault, a more "ostentatious" word. That difference is not invariable.