Strictly speaking of brown egg laying rates, the best brown egg layers are as follows:
1, Sex Link hens--5-6 eggs per week per hen (My Black Sex Links have been slightly better layers in cold, dark, winter weather, but both of these hydrids are egg laying machines).
2. Amber Link hens--5 eggs (occasionally 6) per week per hen (These are reverse Red Sex Links, produced by crossing a white/silver gene rooster with a red gene hen).
3. Black Australorp hens--about 5 eggs per week per hen (Until it was broken in 1979, a Black Australorp hen held the world laying record with 364 eggs in 365 days, and while none of mine have reached that kind of laying rate, I have had a few of them lay over 300 eggs in a year).
3. Production Red hens--about 5 eggs per week per hen (These are hybrids produced by crossing Rhode Island Reds with New Hampshire Reds)
3. Rhode Island Red hens--4 to 5 eggs per week per hen
There are other good brown egg laying breeds (Plymouth Rocks, Sussex, Orpingtons, New Hampshire Reds, etc., the list goes on.), but they don't consistently match the laying rates of the previous hens.
Hope this helps.