I’ll weigh in, because my DS faced the same decision two years ago. He’s now happily settled at Case, ME major, has a great internship lined up in Cleveland this summer and plans to live with friends off campus next school year. But he found a lot attractive about State, too.
^^ By and large I agree with what the above posters said. And, OP, I think you have a really good grasp on the differences between the two schools. Short answer, you really can’t go wrong – neither one is better – but it’s important to understand the cultural/atmospheric differences and think where your kid would thrive best.
My DS appreciated being “wooed” by Case; the merit money they gave made it clear he was wanted. And the personal touch with admissions was appreciated. The feeling he got from State was more “OK, come if you like,” with no real acknowledgment of his accomplishments–beyond just the fact of acceptance! It’s a reflection of the relative sizes of the institutions and the public/private difference.
State has brand-new, state-of-the-art, state-funded engineering facilities and a really eye-popping high-tech library. It’s very impressive. On the flip side, there is also a competition for resources-- so many people jostling for the same thing! And Case has ThinkBox, which is also amazing and impressive! Some of the labs are a bit dated, though, my DS has reported.
At State, you’re admitted to engineering but not to a specific major, so you have to pass some hurdles (GPA) and compete for a place in the specific major you want. Not really a problem if your grades are good. At Case you’re admitted to the university as a whole and can choose any major you wish, and switch with minimal red tape.
Will expand on what @Coloradomama said about State being overshadowed by UNC and Duke. I wouldn’t say it’s overshadowed AT ALL. While Duke has a very small and super-selective engineering school that occupies one building, State is “the” publicly funded engineering school for NC. There is a whole huge section of the huge campus that’s devoted to engineering/tech/computers, and the state has poured resources into it. And while UNC-Chapel Hill is the state flagship university, it doesn’t emphasize engineering at all; if you want to be an engineer and stay in state, State is the place! Its reputation in the region is huge.
My DS liked the engineering/techy vibe at State, but he observed that it’s also the state’s center for veterinary medicine and agriculture, so it draws a lot of what he thought of as “country people,” too. Nothing wrong with that, but it wasn’t his thing. Also the rah-rah school spirit is strong there. (Football and basketball both popular.) I will note that engineers generally live together on the engineering campus for first year-- unless they’re in the honors college, which has its own housing.
He felt more drawn to the geekiness/quirkiness of Case. Visiting there, he felt he’d found “his people.” That’s been borne out in the strong and supportive friendships he has made; his whole freshman suite decided to live together again second year. Also there are a lot of collaborative projects in ME where he’s been able to bond with his team. (He works hard, no doubt about it, but he has time to play a D III sport with two practices a week + travel on weekends. He also enjoys the cultural offerings of the Uptown area, including the symphony and art museum; there are similar things in Raleigh, but at Case they’re in walking distance from campus. Cleveland is definitely the better “foodie” town.)
Raleigh is more white-bread American, if I may be blunt, while Cleveland is more gritty. He likes the gritty but also has to be careful about where in Cleveland he goes, and when. Much better public transport in Cleveland, and Case students have “free” (i.e. paid with their student fees) access to the RTA.
Both places have GREAT career fairs and internship opportunities and campus job opportunities. I wouldn’t put one above the other. @Coloradomama is right on about Case; I’ll add that State has access to Research Triangle Park, a center of high-tech jobs for the south. (Oh, she did say that, didn’t she!-- she knows her stuff. 
)
Carolina weather wins, hands down, except that my southern boy was excited about seeing snow and experiencing a new climate. There is lots of cold cold rain in Cleveland, raw windy days. Carolina winters are mild; summer heat and humidity can be brutal, but your DS may not be in school in summer! And there’s AC everywhere.
Agree with @SweetTea about the alumni scholarships. They are plentiful and will help defray costs for the last two years at Case.
I could go on and on. Heck, I have gone on and on! I’ll be glad to answer more questions here or via PM. Best of luck to you and your DS in deciding between two really excellent options.