I actually don't see much difference. You might be able to crank things up faster on a tangential, I don't have one so I don't have that much experience actually using one on any scale, but I don't wire and extract mediums in a radial all the time.
Read the old ABC XYZ of Bee Culture and you'll see that wire was not invented to aid extracting, it was to keep the foundation from sagging until it was drawn.
"SAGGING OF THE FOUNDATION, AND HOW TO PREVENT IT.
Many devices have been tried to prevent the sagging of the foundation, and consequently slight elongation of the cells, in the upper part of the comb. With the L. frames, this is so slight that it occasions no serious trouble with the greater part of the wax of commerce; but with deeper frames, or with some specimens of natural wax, the sagging is sufficient to allow the bees to raise drones in the upper cells. Paper has been tried, and succeeds beautifully, while the bees are getting honey; but during dearth, when they have nothing to do, they are liable at any time to tear the nice combs all to bits, to get out the paper, which I have supposed they imagine to be the web of the moth-worm. In our apiary I have beautiful combs built on thin wood; but as the bottom of the cell is flat, they are compelled to use wax to fill out the interstices, and the value of this surplus wax, it seems to me, throws the wood base entirely out of the question. I do not like the foundation with wire rolled in it, on account of the greater expense, and because we cannot fasten it in the frames as securely as we can where the wires are first sewed through the frames."--ABC and XYZ of BEEKEEPING, A.I. Root – 1891, section on "Comb Foundation"