We've flown several times with DD since 4mths old until recently (2 years old).
She was definitely easier to fly with as a little baby, as she just slept for most of it.
The latest flight we did was just before her 2nd birthday. We flew domestically from Brisbane to Sydney, and then Sydney to Hong Kong, and she was on laps the whole way.
Big mistake. For the return flights we ended up booking an extra seat for her, which worked fine. When she was on our laps she couldn't turn over into the 'head down bum up' sleeping position, and she got upset as she couldn't sleep properly.
In her own chair, we wedged pillows around her, so she was 'in place' like in a car seat, and we loaded up the tablet with Dora and her favourite TV. Worked perfectly, and she slept like that too.
A pilot we met recommended taking a car seat too, as they're used to sleeping in those.