Which fabric is cooler?
Because the 100% cotton and the polyester are both breathable, and because the shirts are ventilated with mesh panels in the sides, there is very little to choose between them. Because the cotton is more absorbent of moisture, it soaks up your sweat on those hot and humid days, so you may possibly feel marginally cooler, even though the shirt then becomes damper. The polyester is a quicker drying fabric, so that may make it more comfortable.
So like everything else in life you have to weigh up the pros and cons, and decide which is most important to you.