I think it's funny to read these comments and think to myself, "I always fly whenever the ticket is cheaper." I usually don't have much to choose from--if the ticket is at night, it's at night, if it's in the day, it's in the day.
But, anyway, it's a 20-hour flight (of in-air time, not counting time spent on layovers which usually is between 6-10 hours) when we fly back to where I'm from so I pretty much just always have it set in my mind that it's going to be exhausting and overwhelming and then if it happens to be better I'm truly surprised. Flying on United States airlines is the worst too. When I flew with my 1-year-old it was a rough flight. I made the entire trip by myself (well...accompanied by my 1-year-old). He had his own seat coming back to HK but he didn't want to stay in it. All of the usual tricks (toys, games, food, video etc.) didn't do anything for him--he was just about as sick of being on that airplane as I was. The passengers on the plane did not take kindly to walking him around the plane (he was walking on his own by that point) as he tried to grab at things on their tables and was making noise so that wasn't so much fun.
But, basically no matter what it's a full 24-hour period of traveling for us so whether I leave in the AM or PM is kind of inconsequential. It doesn't really matter at that point because in a new environment my children are too excited to sleep. I basically didn't sleep at all the entire flight and he slept just a tiny bit. I was burnt out and exhausted when I got back but then again, that's what I was prepared for so it wasn't a big deal. Thankfully, I had family waiting to help me out after I got back.
I think that the most important is the arrival time in the OP's case. I would book my flight so that I can arrive at night so a strong bed-time routine can be established--for adult and child. It also depends on how long you'll be away for and as carang said how many time zones you're crossing. When I go back to where I'm from I switch days--so my body is on HK daytime and where I'm at is the middle of the night. If you're only going to be there a week then it probably doesn't matter that much to try to get over jetlag but if it's longer then it's good to fall into a routine and adjust your body to the new time zone from the get-go. Also helpful is to get out and get a full dose of sunlight the next morning and eat frequently and on schedule with your destination. Jetlag with little kids--especially if you worked really hard to develop a consistent schedule--can be a real pain. Good luck.