There's not really any discussion about it. The "correct" number is the one on the car. Most tires clearly say "MAX PRESSURE" on the sidewall.

I put "correct" in scare quotes because there's never a single correct pressure. It varies based on a variety of variables, from the car's cargo weight, to temperature, to speed driven.

Inflating your tires to the maximum pressure will make the car run really smooth for a while, as you'd be running on about four square inches of patch. But it's not safe to have that little contact with the road, and it will wear your tires unevenly. Also, if you're pushing the tire's max rating, it's awfully easy to go over, and then you could have worse problems. Underinflating is almost as bad.

But the number marked on the car is far more accurate than the number marked on the tire, since the number marked on the tire was never intended to be a suggested inflation pressure. This is obvious when you consider that a large portion of the criteria to determine air pressure is weight, and cars with vastly different curb weights use the same size tires.