Is hate a more heinous motivation for a crime than revenge?
I assume that you are asking this question in connection to the idea of hate crimes as a separate type of crime that is punished more severely than “regular” crimes. If so, it is clearly possible to argue that hate is a more heinous motivation and one that is more damaging to society as a whole.
One of the bad things about crimes is that they can tear at the social fabric of a society. Society needs to guard against crimes to avoid being pulled apart. The problem with hate crimes is that they pull harder at the fabric of society than crimes of revenge do. Of course, if we allowed revenge crimes to go unpunished, society would be harmed. But revenge is a purely personal motive. Not that many people will tend to feel the need for revenge so keenly as to harm another person. In addition, if my neighbor assaults someone out of revenge, it is not likely to impact me very much.
By contrast, hate crimes are not done out of personal animus. Instead, they are done out of hatred for a particular group of people. This is much more damaging to society. It implies that people of different types cannot live together peacefully. This is very dangerous to society. In addition, hate crimes have the potential to spread. If my neighbor assaults someone else who is of my race or my religion out of hate it does have an impact on me. It makes me feel much less safe. It also makes more generalized racial or religious conflict more likely to occur.
Hate may or may not be more heinous in moral terms, but it is more dangerous to society than revenge.