Hi,
i live in Beijing and am not so familiar with Shanghai.
Air quality is definitely an issue here. I remember when i first arrived how bad i thought it was, now i'm just used to it. Its only when new people arrive and mention it that i remember how bad it is.
I think there has only been a few days of clear blue sky in Beijing this year so far (one was for the national day celebrations, go figure). In general the air is very dusty and dry, and just wait until the sandstorms blow! I couldn't think of a worse place to be than BJ if you got asthma.
Also, everybody smokes, and i'm very aware of this coz im a non-smoker. If you go to a bar/restaurant/coffee shop there will always be smokers, esp. annoying when you're in a restaurant and settling into a nice meal.
Spitting is also very common here, more so than SH.
If you're company is sending you over on an expat package, you can live a great life.
I don't think its very children friendly. There's not a lot of green areas, there's just a few small parks here or there, or some green patches in the apartment complex that you're not supposed to walk on.
All the expat bosses send their kids to the expensive international schools, should definitely get your company to pay for this.
Also keep in mind that bith cities are huge. You could spend a lot of time travelling between work/home/school etc..
I don't mean to be negative, i really enjoy living here. Eat out in restaurants every day, meet loads of new people from all over, travelling, exploring, new life experiences etc.. My experience is that Beijing people are more friendly than shanghai people.
The following is my personal opinion, i don't know much about kids.
In my opinion the kids here lead a lot more sheltered life than back home. The play times are pre-arranged for an hour or 2 than everybody returns to their 200sqm on the 10th or 20th floor. To me it lacks the freedom and spontanaiety i had when growing up.
PM me if you got any more questions