Ask Mr. Smarty Plants

We consider "full sun" to be 6 or more hours of sun daily, part shade 2 to 6 hours and shade, less than 2 hours, regardless of the season. So, let's look at the growing conditions of each:

Morella cerifera (wax myrtle) - 6 to 12 ft., evergreen, high water use, sun or part shade

Prunus caroliniana (Carolina laurelcherry) - 15 to 20 ft. tall, evergreen, medium water use, part shade

So, either of them would probably survive, if not prosper, in the situation you describe. In favor of the wax myrtle, it has fragrant leaves and attracts birds; against it, high water use. For the cherry laurel, it also attracts birds, and has only medium water use.  Some plants are not particularly affected by the allelopathy of oaks, but there are no definitive facts on which (or neither) of these plants could get along under the oak. From personal experience, we can tell you we have had cherry laurel grow very well under oaks. In this case, the oaks were native to the property, and the cherry laurel apparently planted by birds. The cherry laurel was pretty slow-growing, but didn't seem prone to disease or insects. 

You're really the only one that can make the choice, based on the conditions you have and what you are looking for in results.  According to this USDA Plant Profile, wax myrtle tends to grow natively more in East Texas, but some are definitely found in the area of Travis County. Then, this USDA Plant Profile for cherry laurel shows pretty much the same thing, but our personal experience was in North Central Texas so it should be okay in Central Texas.

From our Native Plant Profile:

Morella cerifera

Morella cerifera

Prunus caroliniana

Prunus caroliniana