Aldodrake, Hillsborough is a cute town and Orange County schools are pretty good. The make up of the population there is more "country" than Chapel Hill Carrboro City Schools. Maybe not quite as country as Southern Alamance High where my kid is currently taking driver's ed and the student parking lot is full of pick up trucks, but you'd definitely have a lot more rural kids than in Chapel Hill High, ECHHS or Carrboro High.
My kids go to Hawbridge, a charter school in Alamance County. Charters are something you might look at, too. Up until recently we have not had many for profit charters in NC. The one my kids go to is a non-profit and not run by one of the corporations making money off education. My older kid has anxiety and we felt like she needed a smaller school environment. I am envious of the classes and opportunities that kids get at Chapel Hill Carrboro City Schools, though, which is where we would be going, but I think this school is a better fit for my kid.
I think Guilford County has some very good schools, but I would guess Chapel Hill Carrboro schools are probably more similar to Madison's than Guilford County Schools. CHCCS is smaller than Madison's district (CHCCS is about half the size 12,000; google says Madison's is about 25,000). Guilford County is larger (about 3 times as big at 75,000). Orange County School system (Hillsborough) is smaller than Chapel Hill's (about half the size, 7400 students).
There is a culture of achievement at CHCCS that some kids and parents report can be very stressful to susceptible kids. Certain high-achieving kids can get caught up in grades and class rank, etc., but there are a lot of opportunities available through the school system that you can't get in a lot of other public schools in NC. The high taxes in Chapel Hill and Carrboro mainly go to things like our schools. Highly gifted kids are served pretty well in CHCCS. Some folks report that just average kids can fall through the cracks a little. We have a fairly sizable Latino/a population in the schools and a good number of refugees from Burma. When my kids were in elementary school, Carrboro Elementary, everything was translated into Spanish (it's a dual language school) and at that time there were a lot of refugees from Burma there, too, and everything was also translated into Karen. A new school was built and things have shuffled a bit since my kids were there and and I think most of the Burmese and Karen kids are at another elementary now.
For your kids, they could be in a Spanish or Mandarin dual language program in CHCCS schools. I don't believe Orange County Schools (Hillsborough) offer that. Guilford County Schools, as a bigger system, do have a
variety of magnet programs at the elementary level, although I don't know if they offer Mandarin.
Orange County Schools do have a 1 to 1 laptop initiative, where every student 3-12th grade has a laptop and middle and high school students can take it home and to do their school work.
There are also a lot of opportunities in CHCCS like trips to China, Belgium and France, and Costa Rica — all through the middle school my kids would have attended (not that any of that would have worked for my kid with anxiety, but a neighbor kid went to China in 7th grade with her teacher and classmates). The charter we go to is going to Carowinds in Charlotte in May. Just not quite the same.
I think it may come down to how you feel about the different towns. Burlington, Hillsborough, Mebane, Chapel Hill, Carrboro, Browns Summit, and Greensboro are all pretty different. Once you get down here and can look around a bit I think you'll start to feel more at home in one place.
You might try just googling the place name and then looking at what google images brings up. I'm a visual person and that helps me kind of get a feel for a place. I'd say what I see when I google the places we've been talking about definitely corresponds to my experience of those places. (BTW, Madison looks really cool when I do that and now I want to go visit!)