COL Townsend Whelen stated that aperture sights are as good as a scope out to 250 yards or so, PROVIDED you can see the target plainly.

I have shot military silhouette targets all the way out to 800 yards with my M1 Garand and hit them! It of course has an aperture rear sight!

(BTW, "peep" sights are iron sights, but they are NOT "open sights". Some jurisdictions that require "open sights" during some seasons do not permit aperture sights......)