I don't have much to offer, as far as specifics. But our public school had clusters, then a separate gifted program, all in the same building. I strongly felt that the key difference between the "regular" gifted (or high-achieving/high-intelligence) cluster and the actual gifted program was what kind of learning and work style a kid had, yet placement decisions were based entirely upon achievement testing.
Our middle son was placed in the separate gifted program, but struggled with responsible usage of all the free time and independence he was given, in terms of completing long-term work. He actually did better, when we took him out and put him in a "regular" classroom, because there was more structure imposed upon him and more regulation of his time-management.
Meanwhile, my friend's son did not quite test high enough to get into the separate gifted program, but was bored in the regular classroom and works very well independently. She fought for an appeal - even though she was made to feel like a problem parent, over it. For whatever reason (possibly just because she was a squeaky wheel), her son did end up in the separate gifted program and has done well.
I think if you're sure your child would do better in the other environment, you should fight for it. No one else will ever be as motivated to advocate for your child, as you are.