Agree on Big Daddy's - the "beef potato" is excellent. I am amazed that it is not a staple in all BBQ places.
You also need to try Elmer's near 41st and Peoria. The "Badwhich" is the thing to order. Their slogan is "It be bad!", and it is. Elmer died a couple of years ago and I believe a relative now owns it. It is not the same in terms of quantity, but still a good deal. You need to try it.