I have sons at both academies. They are completely different experiences.
At Navy, you can fly under the radar during Plebe summer as the class is so big. Lots of majors available and ability to switch within first year. Large campus with great athletic facilities. Great town right outside of the yard if you need a break- note, however that Plebes get few opportunities to leave campus even on weekends their first year. Huge faculty, which means my son has had a number of first-year profs who have struggled connecting with students. First class, top tier athletics programs who play top tier competition. Lots of service selections from flying to cyber to intelligence to super-elite special operations. Tradition, history and great speakers who come to campus. Lots of street cred with civilians- "oooh he went to Annapolis." Poorer reputation for USNA graduates in the fleet- sometimes enlisted sailors see USNA grads as elitist / entitled when compared to NROTC officers.
Coast Guard is much smaller so it is infinitely harder to fly under the radar during swab summer. If you mess up, they will see it. Fewer majors. Smaller campus - pretty in its own NE, red brick, kinda way. Not much to do in New London and not much within walking distance to campus. Coast Guard gets MANY more free weekends swab year. (My USNA son was shocked his CGA brother has so many weekends off). Fewer service selections but overall better places where you will be stationed. Overall longevity of Coast Guard officers speaks directly to how the work/life balance of the Coast Guard is better than that of the Navy. Less street cred with civilians (lots of folks, especially not on the coasts, don't know there is a CGA). Better reputation with enlisted sailors as nearly every Coast Guard officer attends the academy.
Great education / academic support: Even
Future civilian career: slight edge to USNA only by reputation.
Future Military Career: slight edge to CGA based on officer tenure
Future work / life balance while in military: CGA
Athletics quality: USNA
Athletcis ability to play: CGA
Facility quality: USNA (apples to oranges)
My summary: if you want a top-tier education and are willing to serve 5 years to get it, you should choose USNA. If you want a top tier education and are even considering a long-term career in the military, CGA is the way to go.