UT vs TAMU engineering programs

My son has not yet decided between majoring in math or engineering. (Not totally sure which engineering he would even want…maybe aerospace or nuclear) He is curious about the differences between UT and TAMU, as far as which one will give him his major as a freshman, which one will allow him to switch his major is he chooses to, which school has great advisors and a supportive atmosphere within engineering? Any other input you have is appreciated. He is looking for a little flexibility, if that’s even possible at a large public university. (Suggestions for other schools is fine but these are his safety schools, so he wants to know which would be better.)

UT Austin: direct admission to major (but may be admitted to the campus but not the major). Changing major may be difficult if the new major is “full”.

Texas A&M: admission to first year engineering. Students later apply (entry to a major or ETAM) to their desired majors. a 3.5 college GPA automatically admits to the desired engineering major, but otherwise the process is competitive by college GPA and essays. Unfortunately, they have not been very transparent recently about which majors are more and less competitive than others; some majors are rumors to accept no students other than the 3.5 college GPA automatic admit students.

In general, the colleges with the most flexibility in changing majors are likely to be one or more of the following (a) wealthy (and typically highly selective, though not all highly selective colleges are that wealthy), so that each department has excess capacity, (b) small, where the size of the overall college limits enrollment more than the departmental capacities, or © less selective, where the rigor of engineering majors means that the less strong students do not choose them because they are hard.

It is typically large state flagships that are in the upper range of selectivity that are most likely to have issues with engineering departments reaching their maximum teaching capacity, so that they have to limit the number of students who can enter or change into the more popular majors.

This is what I suspected. Thanks for confirming. ??