a vasectomy is used when you dont want his sperm but want him to act like a ram and tease the sheep into season - its used with horses to test if mares are in season and will accept a teaser stallion - it saves injuries on expensive stud animals. only the tube is cut/tied, nothing else is taken away.
a castration will remove the inner parts - balls / tubes etc so he will lose the urge to mate and is less likely t act like a ram.
a ram with a vasectomy is as dangerous as an entire ram, behaviour wise.