I used the square brood chamber with Dadant depth frames for several years, but I found that having to build non-standard tops, inner covers, bottom boards, and frames to hold queen excluders was a problem. I decided to use A. N. Draper's solution of standard Langstroth length and width, but greater depth.
Dadant had written that a brood chamber needed 90,000 worker cells for brood rearing and food storage, but I think the queens of his day were not as prolific as those raised now. I also wanted to use only 9 modified Hoffman frames and a dummy board instead of the full ten frames, so I used a frame 13 inches deep. This also allowed me to use 1 and 1/2 Pierco plastic foundations per frame giving 10,280, 5.3mm worker cells per frame.
This brood chamber configuration winters well and builds strong adult populations, and also allows for winter stores sufficient to last until our spring nectar flow without additional feeding when used with a good strain of honey bee. I still am not sure how efficient it is compared with a single deep Langstroth, given that the frames/foundation style requires splicing of the sidebars to get the desired depth, but being retired, and a hobbyist beekeeper, I don't count my time as being worth much.
