Love math (not necessarilly great, and haven't had coffee, so pls point out errors

. Lets compare surface area of a hoop house with a cube.
Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h
The hoop is basically a half cylinder so take that value and divide by 2 (I'm going to assume that you don't need hardware cloth along the ground. (Cue the comments about digging predators.)
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
Treating both the same, we should subtract one of the sides (bottom) again.
So lets play with the numbers, compare an 8x8x8 coop (kinda looks like your photo, 64 sqft) with a 4x16 hoop house (same sqft).
Surface Area of a Hoop house = (100.53 + 100.48)/2 = 100.5 sqft
Surface Area of a Rectangular Prism = 128+128+64 = 320 sqft
So you are looking at basically 3x as much hardware cloth. But you can walk into the cube and 8ft is a little crazy, so that's not a fair comparison. Lets look at a 8x8x4(height) enclosed run
Surface Area of a Rectangular Prism = 2*64 + 2*32+ 2*32 (-64 for floor) = 192
So a stubby 4ft tall coop is still 2x the amount of hardware cloth.
Of course your reality should come into your decision making. Do you want a long coop? Will they be happier with a long area or will they make less use of the 'end' and be happier with a square, What about the other parts, wood, tubing, hog clips, etc those aren't free. The other benefit of a hoop coop is that you can throw a tarp over it and it's covered for rain and light snow. The square one would see water pool and it wouldn't handle the weight of snow well. And of course waste is another issue, how long do the rolls of hardware cloth come in? Lots of other issues too.
/Scott