I live almost smack dab between Nashville and Memphis. I lived in Nashville a few years and in Memphis for about 4 months. I also lived a few years in Jackson (number 13 on the list in the article above) and most of Jackson's crime is a spill over from Memphis. I have no problem going to Nashville but wouldn't go to Memphis if I had to. Just like a previous poster said you can be walking down the street in a nice area and end up in a bad one real quick. Now I maybe a little biased toward Memphis because I lived in one of those bad areas and probably seen way more bad stuff than most.
Nashville isn't bad as far as big cities go. Most of its crime happens in just a few specific areas, and it doesn't take long to figure out where those areas are. Just watch the news for one night. Although in the past few years it seems to be spilling over into some of the nicer areas.
Personally I wouldn't raise a kid in either one of them but would have no problem living in some of the areas around Nashville. Murfreesboro being about 25 miles south of Nashville would be my optimal choice. As for Memphis if I never have to even drive through that gang infested hole again I will be very happy.