Either one should do well. My question is that many Savannahs seem to be planted at the door to frame the door. The problem with that is that wasps and bees literally 'rape' this holly when it flowers in Spring. Getting out the door is like running a gauntlet. Have you considered Mary Nell holly? They can be hard to find, but I have two of them within 12" of solid caliche and have no iron deficiency. The can be shaped once a year and hold it for a long time.

I have the Savannah Holly, and my next door neighbor has the wax myrtle.

The holly has done very well, for me in Lewisville. Steady, slow grower, but they are along the back fence, not close to the house. Their mature size, makes them unsuitable for placement close to the house.

The wax myrtle is a fast grower, that will get away from you, quickly, if not well pruned, regularly. Also best used away from the house. Better for large landscapes, and not city environments, in my opinion.