I don't know if it is useful to compare Mel Gibson with Kanye West, but it does make my life easier to do so.
Both have suffered numerous professional setbacks because of their behavior (although, to be fair, there's no comparison between Kanye and noted woman beater Chris Brown) and both have demonstrated that they have self-control issues.
Kanye has been called a jackass by the President of the United States. Gibson has been called far worse. But this is where the public and private personas come into contrast, and they couldn't be more stark. Privately, Kanye is, reputedly, a very caring and generous person. If you believe what Aziz Ansari says, Kanye is a decent human being who cares about others.
I would never believe Joe Eszterhas about anyone or anything, however. He is what you would call an impeachable source. But if he has tapes of Gibson ranting and raving about Jewish people, I would say that this is a very good example of how Gibson can present a public face that is apologetic and conciliatory while maintaining a private persona that is equal parts jackass and maniac.
Do you know who might have painted the most accurate picture of all? South Park.