I dont' know about pay, but I can comment on lifestyle. I grew up near Nashville and lived outside of Charlotte for several years. I currently live in East Tennesse, about equidistant from both cities.
I disagree that Charlotte is more cosmopolitan. I think Charlotte is very "average" in terms of what a city that size has to offer. I often headed to smaller large towns around me to meet my needs rather than Charlotte because it felt very... forced. It hasn't been a large city for a very long time, so it lacks something unique, in my opinion. I'm sure I'm hurting some lifelong Charlotte residents' feelings and I'm sorry, but that was my experience. They have the banking industry and are attracting lots of people because of it.
Still, Nashville has tons of character. Its an older city with a richer legacy, but it still maintains a cozy feel. I've heard it called "The New Austin" in terms of growth and "coolness." The music industry - beyond country and Christian music - is moving to Nashville. Lots of artistic, creative things have always been happening there. I'm not sure if that's your thing, but it appeals to me.
Also, the landscape in Nashville is prettier than Charlotte, IMO, but neither city is bad. Nashville just has some beautiful rolling hills and natural beauty. Charlotte looks more industrial.
As far as pay, I know that the COL in some areas around Nashville (extending to central and western KY, the rest of TN, north Alabama) is among the lowest in the nation. I would expect it to be a bit higher in Nashville because of its size, but I wouldn't expect it to be better than Charlotte for sure.
Don't get me wrong, Charlotte is fine, but I guess the "more cosmopolitan" argument hooked me. Charlotte is close to Atlanta, Columbia, Raleigh/Durham/Chapel Hill, and the beach. I didn't meet a lot of people who were actually FROM Charlotte, but a lot of people moved in from elsewhere and loved it. It is probably more diverse in the truest sense of the word (in that it has more ethnic groups and nations represented). And if you're into Nascar, then its your town.
I'll admit I'm completely and totally biased toward the south that's west of the Appalachians because its my home.