For some reason, no one else has mentioned that a person firing a gun knows that the recoil will occur when they pull the trigger and will brace themselves against that force, while taking a round into a bulletproof vest is usually a surprising event that the subject hasn't really prepared for.

It's akin to a person in a physical confrontation might easily brace against an obvious shove from someone in front of them, while an identical shove coming suddenly behind would knock them over.