Not the right question
I imagine that all 3 academies would have stellar engineering programs, but I'm wondering if one is typically thought of as the "best."
Thanks!
All three academies have fine, highly ranked engineering programs, and will prepare you for a career in the military as well. Beyond that, 'best' is going to be largely a matter of perception. Any of the academies can prepare you to work as an engineer, as can any of the highly rated non-military schools, or for that matter, lots of state schools. No matter how good the school, you'll probably learn more in your first year working as an engineer, which might or might not be what you do as an Academy graduate.
If you attend an academy, graduate and take your commission, you might end up as a fighter pilot, a platoon leader in the Marines, a Navy intelligence officer, etc., jobs which might use some or none of the engineering skills you'd learn getting your degree. The chances you'd get a job designing planes is extremely remote.
If you get out after five years or 20 as an officer, you might need to refresh your engineering skills if you want to work as an engineer, but the leadership skills, top secret clearance, and other things you'll pick up along the way will make you much more employable.
If you really want to work as an aeronautical engineer, you might be better off with a degree from a civilian school like Stanford or MIT, and applying to Northrop-Grumman or Lockheed. If you want to be a leader, serve your country, do something that really matters, an academy might be for you.