We always fly, but we kind of face the same dilemma. Fly out on an early flight or fly out late the night before.
We used to always fly out in the morning on a Saturday. We would be up super early, have all the "hassles/stress" of travelling, finally get too Disney, get checked in and be absolutely exhausted that first day. We would then push ourselves that first night because hey we are in Disney. Then be tired and cranky the next day. It would take a few days to get that right balance of rested for Disney touring.
The last 3-4 trips, we take a late Friday flight out. Yes that day is super long and tiring, but we get all the travelling done and over with. We don't make any major plans our first morning and sleep in. We are well rested and ready to go then....usually by about noon. DS still wakes up early, but we kind of funk around the resort and get into "vacation mode". There is no travel tiredness carrying into other days of our vacation.
With driving, I would try to drive all the way to Disney. That extra hour probably won't make a huge difference. I like to check right into my resort even though it is super late, but if you can't afford that there are lots of gorgeous and cheap offsite properties right there to stay at that first night. Sleep in, grab a breakfast or lunch, then head over to your resort and check in. You will be well rested and ready to go by mid afternoon. If you drove in that morning, you will be cranky and tired. Even if the kids sleep in the car (and that is a big IF) it isn't the same as getting a good nights sleep in a bed.