Definitely a parents lack of control. I just flew by myself with my 3 small children. 8, 6 and 4. Frankfurt to MCO. Over 10 hour flight. Kids were fantastic - I even had 3 different people tell me so. My 4 yr old had a small meltdown period but was very brief and a suggested visit to the bathroom cured all. ( his AVOD was not working for 2 hours - go figure)
Then from MCO - IAD - LAS. Great again. I was very pleased with the way they travelled but I would be lying if I said I was not nervous the whole time
As far as children in first/business. Parents know their children best. I would travel in first/business with my children as I know I can control them. If I knew that it would be difficult to control the child I would have the decency to fly economy, knowing how much one had paid to enjoy a more relaxed atmosphere in bus/first.