I've a bit over 12,000 mostly off-road miles using 26x8-14 ATV tires on one of my TWs.
Their width occasionally reveals some atypical behavior; things like on firm sidehills where you might notice sidewall contact is occurring a bit further from under center line of bike requiring a bit more weight shift.
Tire's width when it exceeds that of narrow, deep ruts made by MX grade knobbies means ATV tire does not drop to bottom and act like a slot ca. Instead rear can dart a bit from side to side seeking an equilibrium giving the impression of a drunken sailor. So there might be a slight loss of stability but I don't mind due to traction improvements in marginal conditions.
My one TW with the ATV tire does well in mud, sand & snow conditions that tend to cause grief to the other TrailWing equipped TW. Had I completed today's ride on the stock tire TW I would have spun the tire a lot and made a mess of some otherwise nice trail sections.
Once again these issues are lessened with a rounder profile like the Duro2 or my Terracross. My Terracross can be made to slid around somewhat playfully but my original Duro's squarish profile wasn't so linearly predictable...try to get the original Duro up on sharp sidewall edges and feed in power with good balance and it just wants to make even more traction, stand up and go a bit ballistic. Get the balance wrong and it can quickly slide out instead. Doable, just a bit more demanding than a rounder profile tire. Just like TW-Brian's RipSaw equipped TW he let me ride up one rooted trail the square edge tires seem to be happiest just making gobs of forward traction.
When conditions are firm and dry the ATV tire gives few benefits other than aggressive looks. Downsides include slower acceleration and reduced fuel mileage due to weight and rolling resistance imparted by low air pressures we typically operate at.
It is said that they certainly handle better with no air pressure than a conventional TrailWing with a puncture.
I can only confirm this comparison at 4psi for each.
