I only fly Southwest (as long as it goes to my destination). I find base prices to be more or less the same as other airlines--or even slightly lower--but then two free bags on top of that makes it a WAY better deal. It's not even close. Checked bags elsewhere are $30 each now, and 2x that round trip is an extra $120 -- that's the price of the ticket itself for most west coast trips. Even when I only need one checked bag, it's a no-brainer to use Southwest. Then on top of that, there's no charge for change fees, whereas the other airlines charge a ridiculous $150 or higher.
To be honest, I don't know how other airlines compete for the same routes...but I still see them all the time, so I guess they're doing it somehow.