It does come up a lot. The answer to my mind is a bit like saying do people do more harm than good? Because it is people that follow religions and people that don't follow religiions if you see what I'm saying.
I don't think it is religions as such that do the harm, it is the people. It's as simple as that. Some people do good some people do harm whatever their religion may happen to be.
Religion is just a tool, a crutch, something to hang your philosophical and moral hat on so to speak. If the person following a particular religion gets all the positive life enhancing moral lessons that can be had and lead good lives, then generally I would say they are going to do good not harm, but if they get the wrong message or become negative in their thinking because of the religion they are following and end up hating everyone who isn't like them then yes, they are going to do a lot of harm.
Good intentions in this world have led a lot of people astray in my opinion.