RIRMy Barred Rocks have been my best layers, by far. My mother has them too with the same experience. 6-7 eggs per day as pullets and 5-6 a day season 2-4 so far, 9 months out of the year. Obviously they slow down before and during molt and mine slow down to the occasional egg during the coldest two months of the year and start to slowly work up from there.
Next in line are my RIR's. 5-7 eggs per week per bird but it does range more than my BR's. They slow down a lot more abruptly in the winter but they ramp up production faster too.
My Australorps are probably about the same as my RIR's or not far off. I only have a few so it is harder to tell and they are in the mixed flock not one of the separates.
My easter eggers are next. 4-5 eggs a week after their pullet years. They slow down to 2-3 per week in the winter but I have NEVER had them stop laying. That is great because for some reason I like their eggs more...lol. I know, that is mental. Sorry, these are not brown eggs and I know you are asking for those but this is where this bird fits in my lineup.
Next to last is my Orpington flock. These ladies were very slow to mature. I got my first egg at 26 weeks and not everyone started laying until about 28 weeks or so. They did lay right through their first winter as per normal with birds that I have raised. They did so by giving me 4-6 eggs per week per bird and like the RIR's there seemed to be more variance here than with some other birds. Now that they are going into their third season and working on their fourth I am getting, on average, 4-5 eggs per week per bird but 4 is more common. They stop laying almost completely from December to February. I get the random egg now and again. But come the first week of March they are right back to 4-5 eggs per week.
I have more breeds on their way to test out over the next 3-4 seasons.
Disclaimer, all of my birds are hatchery quality. Not all of them from the same hatchery. I have mostly cackle birds but I get TSC birds and I have no idea where they come from and I have some from Meyer too.