On the M16/M4 family the large aperture is labeled 0-2 and is used for targets out to 200 meters (if the rifle was zeroed at 300) and the small, unmarked, long range aperture is used at 300 and beyond using the range wheel on the rear sight.
Obviously these sights are calibrated for 5.56mm projectiles running roughly 3000 feet per second and not .22LR at maybe 1000 fps.
On the M4 Carbine the center of the 0-2 aperture is about 4 MOA lower than the unmarked aperture, about 4 clicks on the elevation. At 25 yards that's 1/4" per click or 1" difference switching the apertures.
Zero the rifle at 25 yards with the small aperture. Then flip the sight forward so 0-2 shows and see where she prints. the M4 carbine will shoot 1" low, but it's firing 5.56mm.
Good shooting stock weld on these rifles places the tip of your nose against the back of the charging handle. This is about the only way to get consistent eye placement behind the rear sight. With your eye this close to the rear sight the smaller aperture is plenty big and is more accurate because it's smaller.
You'll probably need the stock in at least two notches to shoot nose-to-charging-handle comfortably. The stock is too long to start with and the M&P15-22 lower even longer than the M4 pushing the buttstock out even farther from the rear sight.
With a .22LR at maybe 50 yards and the proper shooting position you'll find the small aperture quite accurate and easy to see thru. 50 yards makes a good "battlesight" for this rifle as well.
-- Chuck