My Dad and his brothers, as far as I can recall, used barge boxes, with two sets of 12" side and back extenstions, and a set of flares, but I have dim memories of my uncles having flare boxes (make unknown) on Electric running gears, before they were replaced with JD varnished wood boxes on JD gears.
My Dad had two Heider wood boxes and an Anthony steel box, all on Westendorf gears.
There are no corners to clean out on the flare boxes. But they are a smaller "target" to hit with the elevator on the picker (especially the smaller 100 bushel ones). That's why many flare boxes had "flare" sideboards on them. We always used flare boxes (and still do mostly) when we picked most of our corn in ear back in the 70's and early 80's. But we had the larger & wider 165 bushel wagons so we didn't have flare boards on them.
I grew up with barge boxes. My dad had only one until I was old enough to drive the corn wagon to the elevator and unload it myself. Then we got a nice Lundell 6x12 box on a Lundell gear. I wish I had that box back--IF any one knows of one let me know.
Since my dad has retired and my hobby of corn pickers has grown, I do have a MN flare box. I don't have lots of experience with the flare box, but I do agree you don't have the corners to deal with as you clean out the corners on a barge box.
For me, I like the barge wagon-nostalgia. Check out other posts on barge wagons for pictures of the ones I have. My collection of them continues to grow. I have one that I am currently priming and painting, so hopefully pictures to add as soon as I get it done. I have 3 particular ones I am looking for, but don't shy away from a good buy on one!