very long flights with children

Is it better to do a nonstop flight (11-hour overnight flight) or break it up with one layover, which would end up being a 14-16 hour trip --not including getting to JFK, boarding, etc.  Advice appreciated!

A friend just did this last month with 2 kids, aged 3 and 2 from Newark to HK and back. Non stop, overnight. She prepped the kids so that they were well rested but would go down to sleep early into the flight. They were great. She had tons of entertainment readily available. Though my brother just flew Etihad from Kenya to US and he wasn't allowed a laptop or iPad or any electronics on board besides a phone, so look into that for your flight. I know electronics can keep kids busy. Good luck. 

Definitely nonstop--for overnight, pick the latest departure you can to maximize sleep potential. With the earlier departures (5-6ish), they keep the lights on for a good portion of the flight with dinner service etc.

Also with a connection, you risk an even longer trip due to delays with the connecting flight if there is weather/traffic etc. The long haul carriers are given priority and are less likely to have delays.