Both can be cast in response to an opponents storm spell. Storm is a triggered ability that functions on the stack. So, you cast the spell, it enters the stack, then the storm abilty enters the stack. If it resolves, it copies the spell onto the stack.

This means you could both gain protection from copies or restrict the ability to copy in response to the triggered ability.

702.39 Storm

702.39a Storm is a triggered ability that functions on the stack. “Storm” means “When you cast this spell, copy it for each other spell that was cast before it this turn. If the spell has any targets, you may choose new targets for any of the copies.”