If i had to choose from these two i would choose the spiritual route but see no reason why there cannot be different levels that would allow for both -
physical would be like mega heros/villains of legend that mortals have a hard time dealing with (if at all possible) - EX: Hercules, legendary Pyro, the cyclopes.
spiritual would be full powered gods that can only interact through the actions of mortals - Olympians, Norse, etc.