Your new truck may sit higher than the old one and be causing your trailer to tow with the nose high. You might have to lower the hitch head on your shank one hole to compensate. Towing nose high tends to cause a trailer to be less stable in many cases. Check to see that your trailer is level or slightly nose down. If not, adjust your hitch.
Another cause of the different towing action may be the new tires on the new truck. Often, new tires are "squirmy" which causes weird towing feelings and will settle down once the newness wears off. Check tire pressures also.
Barney