There is a reason people will scream MIT. If you want to do any engineering, it is generally the superior choice, esp for the fields you mention. You should visit MIT you can. The course work, esp. in the areas you mentioned is quite rigorous, but you will graduate ready to work (although many engineers get masters) with an engineering degree everyone respects (if not considered the best in the world).
While MIT requires some humanities, you won’t have to take too many. The quality of the humanities at MIT are quite high and you will quickly find that most MIT undergrads are well read. Many are heavily engaged in policy, sports, politics and other outside activities.
The Greek life at MIT rivals most schools. Most students who participate in a frat live there at some point, but you can also live on campus. The dorms have their own character that creates a close atmosphere - in most cases.
Being in Boston, which is a major hub for colleges, and a town that is manageable but has all the amenities including culture and sports is hard to beat (but certainly beats New Haven - admittedly I am not a big fan of New Haven). I have had many friends at both schools and generally people are quite happy with their choice, given the criteria you present, I would definitely say MIT. That being said, you will also get a strong education at Yale. Good luck