One of my homegirls from Memphis was just out in Greensboro last month and is considering moving her and her daughter there, same reasons...
What other quality of life factors matter to you? That way I can tell you whether Durm or Clt is a better fit for what you're looking for...
Both cities are similar in terms of violence and crime; Durm is slightly worse than Clt because it's smaller and the hot areas are closer to each other than in Clt, but overall, they not really that different in terms of violence. Durm has a worse historical reputation for crime but both it and Clt are like 3x safer than Memphis, no joke. The worst areas in both cities are not even comparable to the worst areas I'm Memphis...
It's easy to avoid hot areas in the big Carolina cities because the crime isn't pervasive citywide...
Clt around 33.5% black, Durm around 36.3% black, compared to Memphis being like 62.4% black, but both cities are MUCH better cities for black people. You'll see a significantly higher degree of diversity than you ever find in Memphis. Both cities have a stronger black business climate, less black poverty, more black wealth, stronger black middle class, more educated Blacks, and we have representation in both cities on the civic level...
Having lived in both Clt and Memphis it's not even close, Charlotte is 10x the city Memphis is. I used to work in Durham and I've otherwise visited many, many times. It isn't my favorite city but my personal tastes may be different from yours. I'd still recommend it to any mobile black folk over Memphis...