Originally Posted by Happy Feet

I was assuming the "all things being equal" part to include tire pressure.

Of course contact patch has nothing to do with the question. We really don't even know what the question is as the Op tends to just ask random things that have no real world application. The genesis was another thread, where he asked if others rode rigid frame mtb's. Some people answered. I posted a pic of the rigid fatbike I mtb with. He mused: "Is a fat bike even a rigid?" Hence, a thread in a different sub forum asking vaguely if fat tires equal suspension.

Mostly it's a useless question without any clarification. Do fatter tires offer more "suspension" than skinny tires?

If asking in regards to road bikes and differentiating between say, a 23mm or 32mm 700c tire the answer is obvious.
If asking in regards to all roads / gravel / rail / flow trails, differentiating between say, a 1.75" or 4" 26" tire the answer is again obvious.
And, if asking about technical off road and differentiating between say, a full suspension mtb or rigid fatbike the answer is also obvious.

What is not obvious is when the question is asked just vaguely enough so that respondents argue details like tire pressure from different application POV's. Then the OP can sit back and watch the fun. One big give away is that he never clarifies the questions when asked and just randomly complements posters or parachutes comments to encourage the nonsensical debate. They are just stream of consciousness questions asked out loud.