I have hunted grouse for more than thirty-five years. In that time I have owned a bunch of guns in search of the best grouse gun for myself. This choice is a very personal thing. What I've found is the ones that work best for me are not too light and not too heavy. I like a stock that is a little shorter in length of pull than what I am supposed to shoot and prefer 28" barrels. I also like very little choke constriction as I shoot over pointing dogs and seldom have a shot of more than 25 yards.
My most effective grouse gun was a 12 gauge, Webley & Scott with 28" barrels. It weighed 6lb 3oz. and was bored 003 & .007. My second most efficient grouse killer was an original Ruger Red Label choked SK/SK that weighed about 7lbs. Close to the Ruger was a custom stocked M21, 20 gauge.
My least effecient gun I've shot is a Peter Chapman of London, 20 gauge sidelock that weighs 5lb. 3oz. It's just too light and whippy even when grasping the gun with the minnimum of grip pressure.
My grouse hunting partner thinks his custom stocked model 21, 20 gauge is the ideal grouse gun. His weighs under 6-1/2lbs and is bored IC/M. I've watched him kill a whole bunch of grouse over the years and this gun is very lethal in his hands.
I recently started shooting a 20 gauge Browning Superposed "Lightning" choked sk/sk. It's proving to be an effective bird gun too. It weighs between 6-6-1/2lbs.