Given what little I know regarding dry soil conditions in Texas, I would go for the Post Tensioned concrete, which behaves like a bridge that spans the voids in the soil. A slab on grade foundation will probably involve more concrete to make up for the strength issues, so cost is not a real factor in some cases.
Post tensioning involves laying sheathed cables at right angles in the slab area before the slab is poured. The cables run the length of the foundation in each direction, and after the slab has cured for at least a week or two, the contractor comes along with a device that applies ungodly amounts of tension to the cables, placing the concrete under compression. This makes the concrete very stiff and extremely strong. They do this most often in concrete commercial buildings with multiple floors.
The rebar in a regular slab on grade foundation is supposed to create strength when the slab is under tension, by refusing to let the concrete pull apart, but this is not as effective as the post tensioning.
Discuss the options with your builder, the architect, the city permit review office, and the engineer who did the analysis. Do not base your decision solely on initial cost, but consider potential resale implications, construction impacts in terms of project delays, permit issues, etc.
You do have a construction attorney representing you, right?