My family and I will either fly first thing in the AM or last flight of the day, and here's why:
AM:
-With a 7 or 8 a.m. flight, I have to get my DD's (6 & 3) up about 2-3 hrs. before (and depending on where we fly out of, we'll stay at a hotel close to the airport, giving everyone an extra 3 hrs. of sleep...in theory). So...since the girls are up by 4 or 5 a.m., they typically sleep thru the entire flight, which is good news for us parents and fellow passengers! And, they're ready to crash by 9 p.m., sleeping until 8-9 a.m. the following day.
PM:
-Typically, the last flight of the day out of BWI with AirTran (the airline we ALWAYS use), is around 7:30 p.m., getting us into MCO by 9:30-10 p.m.. Sure, the girls will probably be up for most of the flight, if not all, but by the time we hit the hotel, they're ready for bed (with DME, this ends up being close to 11-11:30 p.m.). This later flight allows my DH to get a full work day in and DD6 an entire day of schooling in. The only reason we take a night flight is because we cannot wait to start the "magic" and really enjoy waking up in WDW; but, we basically wasted our DVC points on a few hours of sleep.
In conclusion, AM flights are better for the parents (well, us at least), because the kids sleep; while PM flights are good for everyone in terms of getting another day of work and school in. The very first non-stop flight of the day, in my experience, is almost always full. Mid-day flights (I have taken a couple) were the least crowded, followed by the last non-stop flight of the day.
Basically, it depends on your family dynamic: are you morning people or night owls?
Have fun and don't forget to pack distractions for the kiddos in your carry-on!