Given those choices, Mr. Smarty Plants would have to choose the Yaupon Ilex vomitoria (Yaupon) because it is a native plant, and that's what we are all about here at the Lady Bird Johnson Wildflower Center. The Winter Gem Boxwood (Buxus microphylla japonica), although it is widely used in landscaping, is a native of Japan.
Here are links to three varieties of Dwarf Yaupon
Bordeaux requires full sun
To look for other plants, go to our Native Plant Database, and scroll down to the Combination Search Box. Select Texas under State, Shrub under Habit, and Perennial under Duration. Check Sun under Light requirement, Dry (or the conditions that appliy) under Soil moisture, and 1-3 ft. under Size Characteristics. Click on the Submit combination Search button, and you will get a list 20 native species of plants that meet these criteria. Clicking on the Scientific Name of each plant will bring up its NPIN page which has a description of the plant along with growth characteristics and requirements, and images in most cases.
Here are two plants that you might consider:
Leucophyllum frutescens (Cenizo)
Morella cerifera (Wax myrtle) dwarf wax myrtle