We're planning a third trip to Scotland in May of 2024, hoping to pick up some of the odds and ends we've previously missed, among which are the two mentioned driving routes. We've already done the Bealach na Ba to Applecross, but doing it again is welcome. For those unfamiliar, the NE250 loop covers the northeast coast and the Cairngorms.
I have very similar itineraries that do one route or the other, fitting right into our other ports of call, so the choice doesn't really impact the rest of our trip.
Whichever one we do, the other will probably be done in some distant future trip.
I think both are products of creative marketing by the local towns. I'd guess the NC500 will be busier. If you choose the NC500, which direction? I'd much rather deal with slow traffic coming at me than in front of me.