The Catholic church has a lot of problems, but I generally think out of all Christian sects, they do exorcism the best. Mostly because, as this article points out, the Catholic church actually doesn't see every single case as demonic. And their method of exorcism is usually a lot more gentle and less disturbing than what we see from non-Catholic churches. It really is just a prayer, and as it is pointed out, the priest performing the exorcism is supposed to do all of this in collaboration with the person's medical team.

So many non-Catholic churches have a problem with that last part, where the afflicted are encouraged to go off their meds and disengage from their medical care team.