Prestige really does not matter much, if at all, in engineering. I have worked with graduates from Rutgers (and MIT, and Stanford, and U. Mass Amherst, and many other schools, and in one case GT). On the most part no one cares where anyone got their degree. GT is a very good university. However, you can do very well with a degree from either one of these two very good universities.
When I was applying to graduate schools, I was applying with an undergraduate GPA that was probably only okay because I was coming from a school that is also notorious for grade deflation (specifically MIT). However, if I had been coming from a different university, then I would probably have had a higher undergraduate GPA. I doubt that it would have made much difference one way or another. Certainly the students who I met in graduate school came from a very wide range of universities (including Rutgers).
If you have a strong personal desire to attend GT, and if your parents can afford it, then it might be a reasonable choice. However, given what you have described, unless you have a very strong preference, I would be inclined to stick with Rutgers.