PSIs definitely play a part, and yeah, a lower tire pressure will result in a larger contact patch.
I always end up with a lower PSI up front, partly probably due to my front tires being larger than the rears. But I don't just randomly pick a PSI.
When I'm in the mood to play around or try a new tire, for my rear tire, I'll fill it up to 40 or 45 PSI and begin a climb, then squirt a little air out and ride some more, etc. At some point I'll decide that I went too low, and that's when I'll break out the pressure gauge to see how low I got it two, pump a couple of PSI back in and call it good. It's amazing that (for example) 40 PSI might cause me to break traction of something steep and loose, while 38 sticks like glue.
I'll do the same procedure with my front tire, but under higher speeds and cornering. Too high and it skips around and doesn't hold a line. Too low and it begins to feel sloppy and I can feel it rolling under, like a flat tire on a car. I'm usually anywhere from 8 to 10 to 12 PSI lower in the front compared to the rear.