From a purely scientific standpoint, aka physics, and with all things being the same (especially both tires supporting the same weight and having the same internal air pressure) but excepting the overall diameter, the size of the contact patches will be identical. The contact patches will, however, vary in shape.
But things are not always the same in the real world. As a tire gets taller (or shorter for that matter) the construction of the tire changes (even between the same make and model) as well which ends up distributing the weight its bearing differently. Furthermore, as the volume of the tire changes the need for differing internal pressures may also be required to maintain load carrying capacity and tire shape.