Windsor & Hampton Court

The changing of the guard at Windsor Castle is daily during the summer months from April to July, every other day the rest of the year. Its really just for tourists and they don't bother turning up if it rains. Its not really recommended but it is possible to do both in one day if you are very time poor. Just don't go on a Sunday. Its best to do Windsor first then Hampton Court as Windsor opens and closes earlier than Hampton Court. Windsor opens at 9:45 and most people take about 2 hours to go around without changing of the guard This year they've opened a few add-on tours that take 30-45 minutes. Downside of visiting in the morning is all the coach tours out of London do Windsor first thing to before going onto places like Stonehenge and Oxford late morning. Hampton Court is a more freeform than Windsor. Instead of a set route there are many facets of the castle, its a bit like a theme park with ad-hoc workshops and entertainments scattered throughout the day which you intersperse with the audio tours. There are 3 distinct audio tours covering different parts of the Palace. Both Windsor (and Eton, Runnymede) and Hampton Court deserve a day each and I would have thought most people would enjoy visiting one 'properly' than doing both in a hurried manner in one day.
.. unless you get your satisfaction from ticking off the places the guide books tell you to go or bragging where you have been when back home.

Both sights are definitely worth seeing, but each deserves most of a full day. As Bob says, unless you are just trying to put another check mark on your bucket list choose one and enjoy.

You could take the train from Paddington Station in London to Windsor around 8:45-9am....it's a 35 minute ride..then the ride from Winsor to Hampton Court is 1hr 15minutes......Hampton Court back to London is a 30 minute train ride.