I believe that both these forms are used to express a negative tendence, but I have the feeling that they are not always interchangeable. In particolar, I got the impression that 嫌いがある is also used to refer to somebody's attitude, am I right?
Yeah, you're kind of right. With がち you put emphasis on the fact that something repeatedly happens, while きらいがある focuses on the way things just are or what people do as a result of something. However, you can't use きらいがある with stuff like the weather, while with がち you can.
General example not pertaining to the last sentence:
The first sentence puts emphasis on him frequently ignoring people's opinions, while the second one stresses the fact that he, as a person, has a tendency to ignore them.
I feel like I explained it pretty badly, but I still hope you get something out of it. Just remember, you can't use きらいがある with natural phenomena and for talking about yourself. Well, unless you like judging yourself in third person...