Funny thing: my wife SWEARS my old 16 gauge kicks more than her Mossberg 12 gauge pump.
It's feasible. Probably a lighter gun which makes it feel worse than the same load in a heavier gun. I've read that some mfrs make 16ga loads hot to get more shot or velocity to be closer to competetive with 12. Same problem with giving your wife a "wife size" pistol her first time shooting (ie pocket pistol) even if it's "just" a .380.