I am a twin, with a twin sister, and I have twin boys. I also used to live in Hawaii, and I briefly home schooled.
I suggest putting them in different classrooms at the same school, just to get started. Not because of the academic differences, but for many, many, many other reasons. If one goes into the advanced program, and the other doesn't, they'll be fine as long as you don't get all dramatic about how great twin A is. Also, twin B may be just as smart or smarter than twin A. She may have been dominated by twin A, and has taken her assigned submissive role. Maybe a birth order book would shed more light on it than I can, but usually one twin takes the place as the first born and the other takes on the role as a younger sibling.
I was twin B, and twin A still likes to tell herself she's smarter because she got told that for so long, and I let her think it's true, just because I feel sorry for her...not everyone can be as smart as twin B!! HA! On a serious note, I hated my "sweetheart role." I felt it was really fake and that I had to dumb it down for the adults because that's what they were expecting. I lost a lot of respect for the adults around me, and I wasn't happy. I didnt feel like I could be "me" because I was the "nice one", while twin A was the "smart one". She, in turn, behaved like a menace.
My twin and I were in the advanced programs, and although it was more enjoyable than the regular program, the kids in the program weren't any smarter than the ones who weren't. They just enjoyed school more, had more motivation, did their homework, etc. Or they had one of those pushy moms who volunteered for everything so her kid would get accepted into the program. I believe a program with mixed levels develops better social skills and prepares children more effectively for real life. In real life, you work with people of all intelligence levels. You have to learn how to utilize human resources, in any group situation, baseball to the board room, and that can only be achieved through diversity of skill.
If you look up IQ's in this country, and figure out the percentage of people who are "gifted" and then look at the percentage of kids in "gifted programs"....there is a suspiciously large number of kids in the gifted programs...OK, so what happened? School made them dumb?
If your kid likes to learn, she will learn everything there is to learn, no matter what school or program she is in. Just add to the equation by finding a great school. It doesn't have to be a private school. In fact, I switched from public school to private school in high school, and wow, those kids were stupid. They had lived in little bubbles. I felt like I was in 6th grade when I was in 9th. It was awful.