if the tires are the same size, then only weight and rolling resistance will be factors.
You know how they advertise "eco-friendly" tires? those tires are low rolling resistance, and although they are typically the same size as the tires replaced, they roll easier do to different tread patterns and rubber compounds. AT tires are heavier (my P-metric destination ATs are only 2lbs more per tire, but LT versions are sometimes 10lbs more per tire), and have tread blocking that is designed to grip on low traction surfaces, there by having a higher rolling resistance.
does this make sense?
maybe 1engineer will correct/suppliment my thoughts here