Whoever is saying SWA is cheapest either doesn't fly enough or doesn't have a clue about the pricing. For my SEA-LAS runs I use United, since I am 1K already.
I cannot stand the cornyness of people on board SWA. I cannot stand the fact that you may buy a last minute fare on SWA and you can end up being the last one to board.

Even in the cases where I pay my own fares, United matches the fare to the WNs. Oh one more thing, SW doesn't know that other countries exist