Recoil can make shotgunning less enjoyable, and it can make you miss, too. It’s easy to get kicked into poor shooting form by a gun that hurts you. In my time coaching high school trap shooters, I have seen kids improve dramatically once they used a softer-shooting gun or load. I have also seen recoil beat young shooters into bad habits, and even seen one who quickly burned out on the sport after one year from too much recoil too soon.
“Recoil” and “kick” are actually two different, but related, things.
Recoil is a factor of gun weight, payload weight and payload velocity. Plug those numbers into a formula (or an online recoil calculator) to find how much a gun recoils, measured in foot/pounds.
Kick, or felt recoil, is more subjective. It’s how that recoil feels when you shoot the gun. Two gun/load combinations with identical recoil can kick differently.