Having lived in the East Midlands for most of my adult life, I can tell you that Nottingham is way better than Derby. In fact Derby-ites are viewed as backwater cousins with knuckle dragging tendencies. The night life in Nottingham is good, the reports of violence are over played its no worse than any other 'big' city.
Having said all that I have recently moved to Breedon, which is in Derbyshire.