The only differences are the intro and capstone courses. At that point, you should apply based on what you want to do outside of your major. In terms of prestige, I think if you’re studying CS, you’re probably going to leave the state. And outside of Michigan, you’ll just be seen as a Michigan grad. Cornell and Berkeley both have CS programs in their liberal arts and engineering schools, but how many people actually know that other than their respective alums? I can almost guarantee most people just view them as Cornell/Berkeley grads rather Cornell Engineering/Berkeley Engineering grads.