I was faced with the same choice and went with AA when I moved here. Most of the reasons have already been covered. Neighbors told me they all used WN, but they don't seem to fly much. I needed something with overseas possibilities and upgrade capabilities.
I have taken non-stops to/from LAX to BNA and to/from LGA. But they are not always convenient, with scheduling changes./ I believe the only current nonstop from LAX departs around 3:00PM, putting you in at BNA well after 10:00PM. For more convenience, even though it sounds counter-intuitive, it is often better to go via DFW or ORD.
Speaking of which: I know I wasn't dreaming when I was able to fly BNA/ORD and ORD/BNA in F last year, M-80, several times. Not anymore. I could be wrong, but if you are flying AA BNA/ORD now, it will be in an RJ, no first class.
The Admiral's Club at BNA is nice, great people.