I could be wrong, but I am wondering if you might be reading the ads too literally (e.g. this tee shirt will wick sweat away from you and keep you comfortable and dry no matter the temperature...). A lot of this is simply "marketing speak".
Summer in Texas? Hot AND humid, right? I guarantee you that you will sweat -- A LOT -- hiking under the sun no matter what tee shirt you wear. Heck, you will sweat profusely even hiking nekkid!
A really good synthetic tee shirt is supposed to first wick moisture away from you, then rapidly evaporate out that moisture. That can work in hot and dry places, but NOT when it's both hot and humid. A cotton shirt will also feel comfy initially as the cotton absorbs the sweat away from your body. But in both cases, synthetic and cotton will soon be overwhelmed and saturated and feel completely wet on you -- the difference being just a small matter of timing.
The actual difference between synthetics and cotton is simply that once you move indoors or rest up in the shade, the synthetic will dry faster whereas the cotton will take much longer to dry. In other words, when hiking and all, you will sweat no matter what -- and your tee shirt will become wet -- but once you get into the shade and stop sweating, the synthetic will dry sooner and thus get you comfortable quicker. I mention synthetics vs. cotton to illustrate what synthetics can and can't do.
My favorite tees are actually the very inexpensive Duofold tees carried by Campmor. They are very comfortable, quick drying -- and unlike some of the more expensive counterparts, they don't exhibit much of a "stink factor". I've worn them for up to five days without any problems or complaints (my hiking buddies are not the polite types).