I've been to both. Would not recommend trying to squeeze both sites into the same day, particularly as you lack your own vehicle and are reliant on trains or buses.
Although some people don't mind spending part of a day at Versailles (generally seeing the inside of the palace and the area of the gardens that are closest to the palace), to really do it justice, it takes about a full day. Especially if you want to really take the time to explore the gardens, Hameau, and other smaller buildings on the grounds. With kids, I would say rent some bikes and really enjoy the grounds. There are also some tours that you could do that have fast track/skip-the-line access to get in (Fat Tire Bikes offers one) and some of those will get you set up with getting out there by train or bus (although it's really easy to do it on your own).
As much as I enjoyed Monet's Gardens/House and the small museum that's on site there, I just really did not see much there that would appeal to kids (particularly younger ones) for an entire day. Naturally, you could spend as much time as you want there and then pack it in and get the train back to Paris, but if you wanted to combine a visit to Giverny with another location in the same day, I would suggest spending the morning in Giverny and then move on by train to Rouen and return to Paris around dinner time. By arriving just before it opened, we were able to tour Monet's Gardens, House, the museum and have a sit down lunch before hopping on a train to Rouen to walk around for a few hours.