Never shot a crossbow so I have no info on them. I have heard though, as jhenderson said, that they can be a pain in the rear to [censored]. If the bad shoulder is your lead arm maybe a lighter compound, or if it's your draw arm, maybe a little lower draw weight? I'm not a huge bow guy, but I am getting back into it this year myself.
"A free people ought not only be armed and disciplined, but they should have sufficient arms and ammunition to maintain a status of independence from any who might attempt to abuse them, which would include their own government."† -- George Washington