Well, I have only read the issues with Resurrection Man, but they are pretty damn uber, IMO.
For one, they are hard to put down. Pretty good healing factor.
Second, they have exotic weaponry they can call on whenever they are on duty. Recently, they fought the Transhuman (dude inside a high tech suit with exotic weaponry and force fields).
At first they couldn't get through the force field, so they loaded ammunition that could. When one of the Body Doubles fought Transhuman, she literally kicked him outside the building and into the parking lot. She stated that they weren't even human, but "Post Human". Whatever that means.
Resurrection Man used his sonic scream, which he said could shatter bone, but they continued to fight him as well.