We've made this trip several times, and although we've flown that last few times we still enjoy the drive.
When we drive we usually leave after work and go as far as Beloit/Janesville Wisconsin. Day 2 is really boring driving as it is mostly through flat or slightly rolling farmland and we stop in the Nashville area.
Day 3 is when we arrive at Disney. By getting the first 5 or so hours out of the way on the first night, it allows us to take a slightly slower pace the rest of the time. We also enjoy stopping at the roadside orange stands and almost always stop at Ruby Falls in Tennessee.
On the way back we spend most of the day at Disney, and then leave late afternoon again to get the first 5 hours out of the way before stopping the first time.
Driving straight through would save a lot of time but it just doesn't seem like vacation as much if we are driving all night, it seems like too much of a chore. We consider the drive and stops along the way to be an integral part of the vacation so this slower pace allows us to see the landmarks and take enough breaks so we don't get on each others nerves.
Also, we found out more about our kids after 24 hours in the car than I can believe. When you are a captive audience for each other, you get around to talking about things that never come up in our busy lifestyles. Another benefit to driving is that the lines for the rides seem more manageable, after sitting in the car for 24 hours, maybe the kids build the patience that is sometimes necessary once you get there.
Also remember that if you have or rent a TV/VCR for the way down, watching a few Disney movies is a lot better way to get in the Disney mood than parking, waiting for your flight, and then sitting packed in a plane for a few hours.
When you fly, the only reason for the transportation is to get you to your destination. When you drive, make sure that the drive becomes part of the fun. You'd be amazed at how much the kids enjoy the little tourist attractions and gift shops on the way down.