Really, I don't have a major preference with either of them, it just depends on your personal preferences and what is important to you.
Southwest has two big advantages - they do not adjust their flight schedule a lot after it is released (which is why they generally wait so much longer to announce their schedule), and they do not charge for the first two pieces of luggage.
One of the major advantages (at least in my mind) with Airtran is the ability to preselect your seats if that matters to you. You don't have to pay the $6 each way if it does not matter to you where you sit, but if you are travelling with small children or are picky about where you like to sit in a plane, you have the option of preselecting your seats. I personally don't like the hastle of making sure I'm at a point where I can go online with SW exactly 24 hours before my flight and register.
We are flying Airtran this trip because (1) they had much better flight times for us than Southwest had, (2) Airtran was considerably cheaper, even when we figure in having to check a couple of bags for our family of 4 and paying for seat fees, and (3) we have two small children and are traveling with some family, and I would rather pay an extra $48 for our trip to ensure that our group all gets to sit together on the plane than risk it with Southwest and have to make sure I check in exactly 24 hours ahead of time to get a good boarding pass.
So, when looking at the cost, be sure to look at the fact that you will have to pay $15 per bag on Airtran (it is more for the second bag per person, but if you are taking more than one large suitcase and one carryon per person, you need to rethink what you are taking to WDW). Also consider whether you want to pay an extra $6 each way (note if you have a layover, you only pay the $6 once - it is $12 roundtrip, no matter how many stops you have). If you don't want to pay that extra fee, that is fine, but you do run the risk of not being able to sit together.
As for the changing flight times - I think that is somewhat overblown with Airtran. It appears that the vast majority of the time, flight times are not changed more than a few minutes, which is typical of almost all airlines. Southwest is very good about not changing flight times, but our schedule is not so structured that Airtran really concerned me that much.
When it comes to overall quality ratings, Airtran was recently ranked 2nd in domestic airlines (behind Hawaiian Airlines) in the 2009 Airline Quality Rating. Southwest was ranked 6th. This study compares on-time ratings, denied boardings (such as an overbooked flight), mishandled bags, and customer complaints.
I know some people swear that Southwest is the best and that Airtran is run by the devil, but in reality they are both very good airlines. You just need to make sure you know what you are getting with both of them.
