I think that the operative difference is the obviously significant weight of the : "very heavy braided military rope...~1" thick", which per foot had to vastly outweigh a similar diameter of a newer rope like the Amsteel Blue (or of the several knockoffs/wannabes I have seen) which per diameter is also massively stronger.
I have broken wire rope/cable, tow chains and straps (despite slow non-kinetic pulling), and the straps behaved very differently from the chains and cable, which which whiplashed dangerously. The strap was limp spaghetti immediately without any spring back, despite the amount of stretch/elasticity it displayed.
I just ordered the Amsteel Blue that has been sitting on my EBay watchlist and Amazon wishlist for over a year because the 20' double-eye ended rope they had in their "garage sale" was half the price of a 25' piece at the regular price, and for my plow winch (a HF 3k-rated cheapie) the 4900# working limit of their 3/16" rope is plenty, and rope that thin will also take up less space on my drum.
For comparison, 3/16" galvanized is typically rated at 3700#, and is stiffer and heavier, though much less expensive at approx $15/1000'.
For me it's,more about the failure rate of the metal cable and having to repair or replace it in 3' of snow while trying to clear the driveway- and of course it always breaks at 0200 (AM) at the far end of the 1000' driveway.
Thomas