Brian ... no, not really.
The big difference that is noticeable is "size" of tub. The round tubs hold 16 gallons of water and the square (both the E and J) hold 18 gallons of water, thus allowing you to wash more clothes at one time.
Also, the Model E with the aluminum tub kept hot water hotter longer. It had a splash "crown" that kept sloshing water in the tub; the N and J do not.
Whether the tub was square or round, the gyrafoam principle of washing was the same. The clothes tumbled toward the center of the tub ... the water currents were forced "through" the clothes instead of the clothes being "pulled" through the water by the agitator. If the machine was loaded correctly the currents were that strong. You can see that principle if you wash just a few clothes at a time.
You know, I've been looking trying to find why Maytag created the square tub; my guess was that it was simpler to create a mold for cast aluminum that way. It was also simpler to have rounded corners on the square tub.
Both round and square tubs slope towards the bottom; creating Maytag's famous sediment zone. Heavy dirt deposits are trapped underneath the agitator so as not be redistributed in the water; water stayed "fresher" for more loads. The operator simply lowered the hose occasionally to drain off the "crud" then she added more hot water and soap and kept on washing. I've never done that; I simply just change the water!! I have the luxury, however, of plenty of hot water and detergent.
I will say this about the square Maytag Model J, however. The Model J (square porcelain tub) was a mid-priced washing machine that was discontinued in 1969 (still not too sure why ... I assume it was because of lack of sales), but I find it to be more "user-friendly" than the N or E. The lid lifts completely off and because it is larger, blankets, rugs, etc., wash really well. It also fits up to square sinks better. I also find that I can stand along the left side of it when wringing and I can easily see behind the wringer. I like to use the J.
Round or square; Maytag conventionals were (and still are for some) a wonderful product.
Did you know that when Maytag was creating their first automatic, one of the criteria was that it washed as well as a Model E? Round automatic vs. square Model E. Go figure.
There's my sales pitch for the day!!
Ben ... you're welcome!!