Given the suspension is good the only difference you should see in tire pressure differences is ride and tire wear.
An E rated tire with stiff enough sidewalls will not change handling from 50 psi to 80 psi on the rear, the front is another story. Depending on the tire, less than 70 psi puts a wallow into the steering at times. The fronts should be aired to acocmodate at least 3/4 of max load all the time or they just don't feel right due to the weight of the engine.
Using the lighter weight rated tires can introduce sway and handling problems UNLESS they are all close to max inflation. The sidewalls on a lot of E rated tires are simply not enough to control the roll from weight of the truck without more air pressure. Inflation tables simply do not take into account the actual vehicle characteristics, not a one size fits all. That and most of these tires are built for Toyotas and 1/2 ton GM's as the target, do not work well on a heavy diesel truck.