I think I'll dig into that question a little.
I think that there is underlying issue of one true religion here. This is a problematic concept. Elitism aside, the followers believing that they only have the privilege get into cognitive dissonance, when they find out that people following other faiths have the same results with their way of exorcism as themselves. Even worse if they are better. The reason is that it puts into question the validity of their privileged position of being in god's favor.
Usually it turns into the others being supported by Devil, so they can explain it out while keeping themselves special. The fact is, if you see yourself special through being better than others, you easily end disillusioned. Someone in the end will be able to do stuff better than you.
Being special by membership is simple tribalism. If you want to be special, make yourself special by developing a skill, that is hard to develop. Banishing spirits is one of the first things one has to master when developing occult/magical/spiritual practice. Practically, you take control of yourself and consequently of your environment. So if I banish, and there are few cases when I did, it was no scary scene like in the horrors, just ritual and done. The jerk was gone. If it wasn't and I had to fight using a lot of my strength, then It's not necessary spirit being powerful, but me not being strong enough to do this effectively.