Both are really good high schools. I have found that the people that live on the east side think it's nicer and the people that live on the west side think it's nicer. The people who have children at Alpharetta High think it's the better school and visa versa. Alpharetta High is newer if that makes a difference. The truth of the matter is that Alpharetta is a great city and there are wonderful neighborhoods in both school districts and both schools are top notch. The following link might be helpful.
You will have to cut and paste bacause I couldn't figure out how to make it link.
If your children have partcular interests you might want to see which school has a better outlet for that. For example, it will be very important to me that the high school that my son goes to has an excellent drama department.... not all schools offer the same extracurricular activites.
I don't know if you live in the area or not, but if you do and have some time before you need to decide, you might want to look at houses in both areas and see which place feels better for you and which is better based on where you and your family will be spending your time. The traffic around here can be challenging and could have an impact on where you decide you want to live.
You will love Alpharetta no matter what part you end up in....it's a great place.