It depends.

As long as AA is flying 762s for this route, they usually will have a lot of capacity to sell. Last year, I wound up spending more on UA, but I picked up more bumps, so it wound up being a wash. (My travel is almost entirely [all but ~5k BIS] leisure and consequently on my own dime.) This year, my pre-bump costs are approximately the same between UA/AA (3.5cpm), while vouchers have driven UA's cost down to about 2cpm... and no, I don't go on mileage runs.

From my observations, walk-up fares on AA tend to peak around $550 each way while the sky is generally the limit for UA. (I don't follow DL prices.)