My kids turned down the gifted middle school that was the same set-up you describe. I think it would have worked extremely well in the core academic subjects. But in the other subjects-- PE, especially, I was concerned and so were my boys. The school has a terrible reputation for bullying (I know two kids who are/have withdrawing because of being bullied), and my boys didn't want to be around that. Fortunately we found what seems to be a great alternative-- we'll find out next year!
In your case, I would definitely opt for the neighborhood school if you can get the principal onboard with differentiation and other challenge.