I live in Chicago, but have been traveling to BNA regularly since 1997 on business. I refuse to fly anything but WN on Chicago-Nashvile, and I have Gold on AA and PremEx on UA. Too many IRROPS to justify higher prices on lousy RJs. In general, AA's mainline route network to points NE of Nashville is garbage since DFW is not a realistic connecting city. You're looking at 2 RJs to virtually anywhere except LGA, BOS, or PHL.

OTOH, Delta's is a bit limited to the west. MEM/CVG are lousy connection cities due to the RJs, so you're looking at Atlanta (lots of service), Detroit, Minneapolis, or the lone non-stop to SLC (6am out, 9pm back).

The wild card is WN. WN has non-stop or one-connection service to a lot of cities, including very good coverage to the west coast.

With all of this in mind, I'd probably pick DL. More cities with F service, far better coverage east of the Mississippi via ATL/DTW, reasonable options to the west coast without backtracking via SLC/MSP. A better chance at getting through your work week without killing somebody, offset by higher redemption rates for when you want to go on vacation. But if you end up doing 40 4-segment trips per year with at least 1/3 of those trips to points west of Nashville, you'd be well-served by getting Platinum on AA as well.