I've had discussions with folks over the years about the contrast between the two different styles of nets. Finally, here's some science to clear the air a bit:
This is a comparison of the square footage of each net style given the maximum span of 5 feet is being used for each.
For a 5' hoop, the rough circumference of the hoop needs to be about 15 feet; this give you a surface area in your net of just over 19 square feet.
For a square net (3'x4') this give you a "carpenters square" of a 5' diagonal span and you only end up with 12 square feet.
Clearly you get an additional 4 square feet of net exposure area giving you a bit of an advantage over the square net.
Personally, I use a "fly-swatter" ultra light net that my father in law built (i contributed very little to the construction, lol) and works famously. We both usually haul em in pretty good but our main advantage is staying in the water.
So there ya have it. Round's vs. Square's = Rounds win.
Good luck to all this upcoming season, I'm getting antsy already and dreaming of the upcoming bouncing nets and wobbling handles.