It seems that both the CSE and ECE departments at Texas A&M offer degrees in Computer Engineering (CE). What is the difference in the CE degrees offered by CSE and ECE? Which department should I apply to?

The Computer Engineering (CE) program at Texas A&M is jointly administered by the CSE and the ECE departments. There are some slight differences in the degree requirements between the two departments. You should select the department by studying faculty web sites and applying to the department with faculty whose interests most closely match yours. You cannot apply to both departments at the same time. Faculty in each department co-advise students in the other department, so if you are admitted to one department and find your closest research match in the other department, you can still work with that faculty member.