As the inflation pressure divided by inner area of the tyre means the force acting on the tyre wall. it is obvious the lower pressure in thicker tyres will produce the same force as higher pressure in skinnier ones. (Or, am I getting that wrong?) In other words, same air force exerted on the tyre walls means the same tyre stiffness, or the same rolling resistance.
What, however, about the fact thicker tyre has bigger contact area with the surface than the skinnier one? Is it not reflected in increased friction? (It is a question because I don't know the answer).
There also is another factor: The tyre tread. I can easily compare 1.75" Smart Sam (a slightly aggressive multi-terrain tyre) to 2" Electrak (slick but soft rubber tyre). Under the same road conditions, I'm achieving high speed on Electraks way easier than on Smart Sams! The difference is quite dramatic. (I use Smart Sams just because they allow me riding in light off-road while Electraks are road only tyres).