A wider tire pumped up to its maximum recommended pressure will typically feel harder than a narrower one when you try to squeeze it by hand. Counter-intuitive, but this is because it actually takes more force to get the same pressure reading in a wider tire, yet the maximum recommended pressures usually don't differ that much between tire widths.

As far as the mushy feeling you get when riding at a somewhat lower pressure, that's got little to do with the actual rolling resistance and speed you'll be able to attain. A harder tire will feel like it's moving faster because you can feel more of the road moving under you.