Recommended pressure always varies. With wider tires, you typically must run them lower, since a too-high pressure will cause the tire to blow off the rim.
If the tire is a stiffer material, this dissipates more energy. In addition, suppler tires deform over obstacles more readily, reducing bouncing and vibration.
More or less, your contact patch is pressure/weight, since the tire can't support much weight on its own. It's going to be almost the same no matter what (slick) tire you are running. Wider tires have less rolling resistance for the same pressure (to a point), since the tire deflects less to maintain the same contact patch. Two tires of the same width, one stiff and one supple, will have to bend in the same way, and have nearly identical contact patches. However, the supple one will dissipate less heat doing this.