Good topic: As I also go BNA once in a while, I find it to be a tough airport to get in and out of, especially from where I am based. I also agree with the PP that while WN gives the most coverage, the flight schedules are just plain odd and not-very-accomodating for business travellers.
At the end of the day, I've tried a few CO-IAH and AA-DFW flights, but for the most part, I've found that getting into BNA is pretty much the same from the west coast: with the exception of WN, you're going to be connecting somehow, somewhere that may not be the most convenient (IAH/DFW makes more sense, at least), so I've just resorted to sticking with US and doing the redeyes to CLT for my EB flights and UA-DEN for my return WB flights. If I go CO/AA I don't have the redeye option, and for redeyes if I'm going to overshoot and connect in ATL, I mind as well connect in CLT with the higher possibility of an UG as a US Plat.
At least from the west coast, I find BNA a particularly hard city to get in to. Not sure what everyone else's experiences are. I'm not the singer-songwriter type, and so the WN timetables are incompatible - with the M&A schedules I'm on.
To the OP: Depends on where you fly, of course. AA has the biggest mainline presence, but if you need east coast coverage or SE coverage, US may serve you in a few places. Those DL BNA-ATL nonstops are VERY expensive. (But then again, so are those US BNA-CLT nonstops). BNA is hard, unless you're strappin' a guitar with "B20" on your BP.