Ron, there is no difference in the disease and vermin carrying capability. Put pigeons together and they all end up with the same stuff.
Now, with that said, I have never heard of anybody catching anything from eating or handling the dead pigeons. The only thing that I personally know of is that when housed together like in a "pigeon coop", there is an accumilation of dander, feces, and god knows what, that mixes together and used to make me and anyone else that was with me start coughing and wheezing. If a person was to be exposed to these conditions constantly, then they would develop chronic symptoms.
My justification was to show why we want to shoot them besides them being good eating. By all means eat them. I would love to eat them but have never been taught how to clean, prepare, and eat the pigeon.