FWIW I have read from multiple sources that WF’s career services is outstanding. That is something to ponder.
I would go with the lower cost option all else being equal.
From the information I could find, UNC is more diverse than Wake Forest (I looked at college navigator, and it said that WFU was 76% white in the fall of 2013 versus 66% white for UNC). However, Wake Forest is more geographically diverse (77% of students are from outside NC), and I have no doubt that Wake Forest is trying to increase diversity.
I guess I don’t really understand the OP’s situation well enough. Does your father have money to pay for UNC? If not, how does he plan to pay for it? If you have to borrow money and he has to borrow a significant amount to pay, then it makes absolutely no sense to go to UNC. Burdening yourself and your family with debt is a very very bad idea. Moreover, as most of the other posters have mentioned, Wake Forest is an excellent school. It is academically challenging and well respected, it’s a beautiful campus, you will be able to establish close relationships with your professors, and I’m certain you will find a group of peers you will establish firm friendships with.
I wouldn’t be the least bit concerned about diversity at either school. I sincerely doubt that both your parents would be so gung-ho about UNC if they thought there was a significant diversity problem there.
Like your parents, I prefer UNC myself. However, it would be crazy to turn down a full ride at Wake. If Wake offers a full ride, go for it.
You can always go to grad school at UNC…go to Wake now.