First, both Scouting and Boy's State are great programs, and Service Academies often report participation in Class Profiles . (As an aside, I don't see Boys State specifically identified in the 2024 or 2025 class profiles, but that doesn't take away from my comments). It's often been reported and debated on SAF that Boy's State carries as much weight as Eagle Scout - I don't know the source of that commentary, but suspect it comes from the West Point study years ago that provided detail about how their Whole Person Multiple is determined, If that is the case, it was years ago, and frankly all candidates should understand that information relating to West Point admissions does not necessarily cross over to USNA. (Yes, we all have the same basic objective, but different services may place more weight on some programs than others).
My personal view, for what its worth -- is that both programs are worth what you put into them. The experiences I had in Boy Scout were invaluable- I had the full resume, Eagle, OA, Patrol Leader, Senior Patrol Leader, Camp Staff, etc, and I credit the experience for much of my success in life. I didn't attend Boys State, in fact barely ever heard of it, but my personal view is that while it is a good, and worthwhile program, you can't get the experiences I had in Scouting in the course of one week. That said, I do believe that the factors that get someone into Boys State, ie. a recognized leader in your school/community, recommended by teachers ,etc. are good indicators of potential success with USNA Admissions.
That said, OP's suggestion that he attend Boy's State to replace Scouting on his application is a non sequitur . They are two different programs, and Service Academies (at least USNA) doesn't check the block as an either /or. I think its probably safe to say that no one ever got into a Service Academy because of either Boys State or Scouting -- perhaps its been the tie breaker in close calls when Noms and Appointments has to pick between two closely ranked candidates, but there are many, many other factors that can be considered. Bottom line -- attend Boys State, or participate in Scouting if that is something that interests you -- its' what you make of the program that counts, not just checking the block.