As much as I have cut back on my use of the AA program to collect miles, the elite status on AA carriers me in ways that SWA status would not. And with AA's tie-ins with Alaska and JetBlue and its international alliance partners, AA works better for me. But if the only flying I was doing was on SWA routes and I had no interest/opportunity to go beyond SWA's network, then SWA could be just fine -- especially if getting great value out of the companion pass.
It could be that you could easily pull off things well with both SWA and American, and that may work out as well or better than putting all your eggs in one basket.