i dont know if we will have time to see both. which is better? we also have kids, so i think they would think the maze at hampton court is cool. but there is the orangerie and the princess diana play area at kensington.
Hampton Court!!!!! Its a great experience, there are so many different rooms which are laid out as they would have been, with a great audio guide. The kitchens and surrounding rooms are fascinating, plus you have the gardens, maze, old grape vine. Nice cafes and gift shops. Together with the train ride to get there (amd possibly a boat ride back) it is fascinating- at least half a day. Kensington Palace really doesnt have much- not many rooms are open. whenever i have been there, the main displays have been dresses and costumes. Not much of interest to kids or males. (My wife likes it- but its only worth a few hours at best). You can visit Hyde park, Kensington gardens Orangerie etc on your own without visiting the palace. So any of these can be just a quick side trip when you are at harrods, Kensington High Street or whatever
Another vote for Hampton Court,, also hope you get the kids to the Tower of London, suites of armour, crown jewels, and the included Beefeaters Tour is interesting and amusing. If kids are under 10 , then perhaps the Museum of Natural History would be better choice.
Hampton Court is much more impressive. Your kids will never forget the maze. I sure have not. To me there is no comparison.
I don't think the kids will find Kensington Palace interesting at all. Unless they are girls of a certain age who might like the dresses. There are plans to revamp the interiors, but those are probably a ways off.
Hampton Court by a mile, the Gardens are fabulous and it is famously haunted !!