FWIW, here's a neat pressure vs load calculator-
https://www.engineersedge.com/calculators/tire_pressure_vs_load_16251.htm
Agree with
@FaKtor34, re quality of ride on C rated vs E rated. From personal experience, but also thinking it out-
While there will be
some additional stiffness with higher ply, it will be negligible
at the same pressure. The E rated would become noticeably stiffer at higher pressures (north of C rated capabilities), but running both tires at 40 psi, with all other variables being equal, the difference in ride quality should be barely noticeable, if at all. Psychology is a powerful thing.
The primary reason I would be after C rated, would be less weight at the corners, affecting takeoff/power, and secondarily, MPG. And as also noted above, if max load of tire, at max pressure, is already at/near max load of truck, why add unnecessary weight at corners. Looks like the E rated AT4W do have the duraspec sidewalls if you think you need the puncture protection. But seems to be mostly a matter of C rated loads being less common at ~35" tires than E rated.
All of that said, I do like the idea of those C rated 35x11.5x18 AT4W's, when it comes time to replace my current. Hadn't noticed that availability before. Even have the same tread depth (18/32) as the 285/75 and 295/70, and at 5 lb and 7 lb lighter respectively.