I guess it depends on what kind of child you have and what kind of parent you are. My two know better than to act up. If it looks like that is about to happen, I march them to the back of the plane and we have a serious chat.
Just once, we were upgraded to First Class, Row 1. I was in heaven. Honey was 3 years old. She was excited because the steward promised her a make-your-own Haagen Daaz ice cream sundae later in the 7-hour flight. She read, she played peek-a-boo with the people behind us, she listened to her own Walkman and then she fell fast asleep. She missed her ice cream.
I have noticed that some of the people in First and Business Class have those noise-excluding headphones by Bose when they know they need sleep or work-time. Everyone has the right to as calm and comfortable flight as they can get, regardless of whether they are rich or poor, whether their seat is paid for out-of-pocket, by their employer or through an upgrade. I would not give up a seat in First or Business Class that I was offered by upgrade. Also, just because a person in Economy who is paying hundreds for their flight, rather than thousands, doesn't mean that they are LESS DESERVING of a good flight.
I have a huge number of flights with kids under my belt; maybe 50 or so. I pack their carry-on bag with what each one needs for 12 hours, just in case of delays. I would never allow my children to shout, kick seats, throw things, play with noisy electronic toys or play with anything that rolls. My kids are not perfect. They sometimes fight about the window seat or who gets to sit next to me or the green marker. They love the movie selection, rarely sleep and seem to make friends of the adults and kids around us. Now we have a DS, which is great.
Flying is very restrictive, stressful and tiring for kids. Infants have it the hardest because of cabin pressure, not being able to express themselves and because they feed off their parent's stress. If it looks like a new mum is trying everything and about to lose it, I sometimes offer to hold a crying baby for a little while, so the lady can go to the loo or just take a breather.
All that being said, I believe that their behaviour is the parent's responsibility whether they are 2 yrs or 12. I do resent parents who just don't seem to care that their kid is bothering everyone around them. Be well-prepared, always pack an extra t-shirt and underpants even for kids up to 10 yrs old (waiting for the loo is really tough 4 some). Put your kitchen chairs into 2 or 3 rows, seat belt on (robe ties work well), perform the "emergency exit" talk just for laughs and practice an "airplane voice" at home for a few days before, every time they talk at high decibels. Should work in First Class, Business class or Economy.