I don't claim to be a great shotgunner but in going through something similar with my old friend (Browning BPS) and new one (Beretta White Onyx) I can tell you without a doubt that stock fit has a whole bunch to do with how well you shoot the gun.

LOP, Cast, Drop, etc.... can have marked effects on your ability to shoot a particular shotgun well.

My advise would be to find a good stock fitter. Go there with your Win and your Browning and let him take a look at both. Chances are that the Win, for whatever reason, fits you better than the Browning. To fix it, he can adjust the stock on the Browning to fit you properly as well.