If Annie Jacobsens research is at all accurate, she mentions that since the 60s they've run simulations constantly to project how a nuclear conflict would escalate, and in that time there's never been a simulation that resulted in an outcome other than complete and total global nuclear exchange. Even from a small scale tactical deployment, simulations always show it escalating to a full cataclysm.

I personally don't have the here-nor-there to say otherwise, but it does seem likely that the type of device doesn't really change the outcome.