I would definitely choose Airtran. Their customer service with us has been nothing but excellent. We missed our return flight from Ft. Lauderdale to DC on 1/2/05 because the cruise ship we were on (ugh, Princess, never again) had trouble with customs and we weren't allowed off of the ship. They told us any flight after 10am was fine, so ours was 10:30, but we couldn't get off the ship till after 9:30 because of this customs thing so we didn't get till the airport till 10:10am so of course we missed the flight (we had checked in online and gotten seats, but we just couldnt' get the bags checked and get through security in time). This was totally not Airtran's fault but they gave us a refund for the return flight since there were no other flights out of that airport on any airline till Thursday (this was a Sunday morning). We had to rent a car and drive to Orlando for a SW flight to Baltimore the next morning and Airtran was very helpful and courteous and gave us a credit for a future flight (which we've already used for our April trip to SC, GA, and WDW!). We have had our price go down on SW many times and have gotten a credit from them, but have NEVER gotten a refund on our credit card. This has happened everytime we have booked with SW and everytime we ask for a refund and have never gotten it.
We have also used their 'upgrade to business class' option ($25 when we did it) and it was very nice. Being able to choose seats is wonderful too, as is the 24 hour check in, not just 12:01am the day of the flight. The SW flight we took from Orlando on 1/3 was at 6:30am. We stayed in that Hyatt at the airport and were checked in for our flight by 5:20am and got B boarding passes. We were right there and got that so I can only imagine that everyone else stayed up till 12:01am to check in online or got to the airport super early since all the A passes were gone 70 minutes before the flight (and the flight was only 2/3 filled). We would have checked in online but were way too tired, especially knowing we had to get up at 5, to stay up till midnight.
We had to go through special security since we bought one way tickets the day before the flight and as such we didn't get to the gate until 6:10, 20 minutes before the flight. By this time, everyone had already boarded and we were literally the last people to get on. We needed a window seat for my daughter's carseat so the only seat available was the last row of the plane, which doesn't recline and makes it tough to install the carseat. The SW flight attendant was very rude and kept telling us we should have gotten there earlier to preboard. The last time we flew SW (to Las Vegas in October because we had leftover money that was going to expire) they only allowed kids under 2 with a carseat to preboard. Not a problem for us since my daughter qualified, but if she were 3 I would have been worried about getting seats together, especially since every seat on the flight was full.
We would still use SW if they had much cheaper rates, but otherwise we choose other airlines. Oh, and Airtran has never changed our flight times. I have heard that form others on this board, but never a problem for us so don't think it will always happen.