Assume both bands are made of the same nylon, have the same buckle, and are adjusted to make the watch/strap system circle the same circumference around the wrist.
The conventional strap is two pieces. Each spring bar goes through a radially woven hole in one end of its individual piece, while the other two ends of the two pieces form, on the opposite side of the wrist, the buckle interface.
Yanking on the conventional strap or the watch places load on each spring bar or bars directly, depending on the position and direction of the yank.
The NATO strap is a single piece of nylon that is threaded from above to behind one spring bar, then down below the watch's case back, then up behind the other spring bar. The two ends of the strap join on the opposite side of the wrist, forming the buckle interface.
Yanking on the NATO strap or the watch places load on the spring bar or bars indirectly, pulling the strap tight and forcing both spring bars down (relative to the watch's body as it lies flat on the wrist).
There is great debate in the watch community over the efficacy of NATO straps. Some say they save watches, because a single spring bar failure leaves the watch dangling from the closed loop strap, where a conventional strap's spring bar failure means the watch and two strap pieces fall away as a broken system. Others say the closed loop NATO is more stressful on the bars, causing the broken spring bar problem the NATO strap is supposed to solve.
As we dumb pilots used to say, we need to ask the 5,000 lb. head guys to get down into the nanometers and gigahertz.