I've flown AA multiple times to and through DFW (to MCO) and I've never had a problem with them. I've never flown Delta or Alaska, so can't compare.
In your other thread, someone pointed out correctly that AA blocks off a bunch of good free coach seats for their frequent-flyer-type passengers, which can make seat selection frustrating. (If you're on points, this may not be an issue, I have no idea.) Flying to MCO this year, the MCO-DFW leg of my flight had no good free aisle/window seats available for selection when I bought my ticket. I just went ahead and selected the available middle seat in a row I wanted and kept watching the flights. Eventually, pretty close to my trip, a good window seat showed up and I switched to it.
You will hear reports of drastic flight time and equipment/seat changes, but I buy my tix about 60-90 days out and my seats have never been changed on me, and my flight times have never moved more than about 15 minutes or so (and often not at all).
I did get "stuck" overnight at DFW this year, but it was not AA's fault (they don't control the severe thunderstorms and tornado warnings). They were good about rebooking me on a flight for the next morning and putting me on standby for a flight later that night (I bailed on standby and just got a hotel room because it was still storming and the standby flight wasn't even there yet at flight time - it ended up leaving at like 10 pm and I'm glad I wasn't on it!). FWIW, all my messed-up flights this year (slight delay leaving home and cancelled/delayed getting back) were American Eagle (the "puddle-jumpers"), but they were good about getting me rebooked when I needed it.
If you're on points, this may not apply, either, but I just buy my tickets OOP. AA prices fluctuate all over the place. You just need to watch them, get an idea of what you're willing to pay, then when you're ready to buy, check them every day and when you see a "good" price, jump on it.
I've flirted with Delta but never taken the plunge; I tried AirTran once back when they still existed and they were fine, but of course they're gone now. I have a couple of other options, but their schedules are very limited and/or go way out of the way for connections to MCO. I keep coming back to AA, and I really have not regretted it.