I had this conversation with a GT graduate about a month ago (I am an MIT graduate). We mostly just came up with similarities (other than winter – better at GT, and summer – better at MIT). To me they are both excellent universities, and they are both only a fit if you want to work hard for four years. Of course I only have experience at one of these universities. However, I would think that they are both excellent (but not equally priced for a Georgia resident).
I am not a big fan of university rankings, but US News does have GT ranked higher than any of the Ivy League schools for general engineering (GT tied at #5, Cornell at #13 in the ranking I was able to find just now).
GT is well respected at least throughout the USA.
The issue of having the GI bill capped at 36 months seems awkward to me. I would not know how to split this between the reality of a student attending university now versus the possibility of a younger sibling attending a different university in the future or the same student or sibling attending grad school in the future.