I agree with everyone's opinions here. They are all meaningful and in the end you should choose what you want. And for some of us, sometimes what you don't know, you get more. So it was for my DS.
My DS also had conflict in schedule. He looked into Boys State for over a year since his Sophomore year after being advised by USMA Admissions to attend if at all possible. Before then, we had no idea about Boys State. After taking the time to learn more about the program and moving things around - summer schedule, DS ended up attending USMA SLE, AFASS, and Boys State. His feedback was, Boys State was the grand finale, and going to Boys State after having gone to Academy programs was absolutely a great combination. He felt like a grown up at Boys State and understood better why the program tied in so well after having gone to Academy summer programs and to his plans to serve the country and to attend a Service Academy. DS said Boys State was his best summer experience last year. And yes he made Eagle Scout and graduated from NYLT summer before his high school freshman year and served in NYLT Camps thereafter, and has been a Council and District Camp Leader/Trainer/SPL, Junior Asst Scoutmaster, Summit Scout and Crew President, Honor Guard, Armorer at JROTC...the list goes on. The point is, if you want it you can manage to fit a lot in to your activities.
But the choice is always yours so follow your heart! If going to DC is what you really want, go for it and don't look back.