Depends on if you are the shooter or the person being hit.
You will have a difficult time convencing a person hit by a bullet that the shooter felt the same impact.
I deal with physics all the time and never gave this any thought.
BUT I have also been in the presence of a couple grown men that were shot as I was next to them. Neither knew they were shot until minutes later. This could be due to caliber, entry area or many other things.
I have read reports from police and medical experts as to what happened after being shot. Most agreed that the caliber shooter used will have a direct bearing on how the person being shot reacts.
That said, I would rather be hit by a .22 than a .50. I would rather be the shooter than the target. No matter the recoil, I could take it better than I could stand the impact.
There are too many variables in such a question. If any variable changes then the results with change.