This isn't an uncommon circumstance. With so few SS weeks, and it with it right after school gets out; and Boy's state in the same time frame; many face this dilemma.
Let's break this down to "Pure Logic". Simplicity is best.
1. Did you contact the academy and ASK if you could switch Summer Seminar dates? Explain that boy's state is the same week, and you'd really like to do both. If you haven't asked; why not?
2. If changing dates isn't an option, then the question is: How sure are you that you want to go to the academy? Specifically the Air Force Academy? If you know "FOR SURE" that you want to go; and you have an idea of what you're getting yourself into; then attending Summer Seminar isn't important. It's designed 100% to sell the academy to the applicant; and to give the applicant a better idea of what they are getting into. But it has zero 0% percent influence on whether or not you receive an appointment or not.
3. Senate Page: Well, that's cool and all, and it is something to put on your application, but it doesn't come close to comparing to Boy/Girl's state.
So; what is my suggestion; (Assuming you asked the academy and they can't change your summer seminar date)....... YOU GO TO BOY'S STATE!!!
You happen to be in a great position. Most applicants don't get to do EITHER. The reason you're in such great shape, is because on your application, especially for your MOC when you're looking for a nomination, you can put down that you APPLIED and WERE ACCEPTED to go to Summer Seminar. This shows you had the initiative and desire to apply. That the academy means a lot to you. And stating basically what I said here; that you were 100% positive you wanted to go to the academy anyway, and summer seminar wasn't going to change your mind in any way; Boy's State seemed like the logical choice to gain some leadership experience and to get a better understand of civics and how our government operates and functions. With this answer; assuming you mean it; applying and being accepted to summer seminar, but going to boy's state instead, will give you just as good of a resume and impression with the MOC nomination board, as if you actually had attended both.
Again; going to summer seminar does absolutely nothing for your academy application. But simply applying, being accepted, and making a MATURE and LOGICAL choice to turn it down in place of Boy's State, will give you many kudos with the MOC Nomination board. Of course, a lot depends on how you PRESENT YOURSELF in your nomination application and interview; as well as your academy application and ALO interview.
Best of luck. Mike