We have flown both and SW blows AT away for service and price. Airtran charges for bags and if you want to choose your seats ahead. It is $6 for each seat and if you change planes, it is $6 to choose on the second leg.
Another thing about AT is that they frequently change your schedule, so you booked a flight at one time and the time may change several times before your trip. It can be a big deal if you have a connecting flight.
We love SW. The service is excellent thru the entire experience. Even the drink service on the flight is smart....they take your order and bring back your drink....no cart blocking the aisle!
The best is, if you have to cancel on SW, you just have a credit of whatever amount you paid for the flight. You have 1 year from the booking date to use the credit. If you can't use it, someone else can.......no fees, no hassles. We found this out on a flight for my mom last summer. I don't know AT's policy, but I suspect it would not be so easy......
That said, AT was safe and we did not have any real problems....but we are SW flyers from now on!