Which is better for a short trip Windsor or Hampton Court or...other?

I wouldn't say either one of those is a "quick 1/2 day". Of those 2 I would choose Hampton Court. It's my favorite day trip out of London. You would need at least 3 hours to see it properly inside and out, plus time there and back I think would be a 5 hour minimum. Windsor is very nice also. You are right that it is a completely different experience from Hampton Court! I would think Windsor would require at least 5 hours also. I really like the town of Windsor which has some very unique shops. With a 10 day trip I would fit both of these into my itinerary!

Windsor is one of my favorite 'day trips'. We have been many, many, many times. IF you plan on doing a full tour of the castle and grounds and adjunct buildings, as well as seeing some of the town and possibly some of Eaton, plan on at least 5-6 hours (including the travel time). If you have already seen the interior of the castle, or have no interest in seeing it this time (it is well worth the time, though, in my opinion- it is my favorite castle), then you could visit for anywhere from 3 - 6 hours and just see the town of Windsor, some of Eaton, possibly do a cruise on the Thames (the boats leave from near the bridge over to Eaton and you get to see the back of the castle and some countryside), and do some shopping. We often would go to Windsor during the day when we had theatre tickets for the evening. Trains leave about every 30 min. from Paddington and return on a similar schedule. It is an easy train ride with a very easy change at Slough and takes about 25 min. Don't worry about buying tickets ahead of time as there is no savings and they are relatively cheap anyway. Whether or not you tour the castle, try to catch a glimpse of the yellow rose garden! It is lovely!

It would be a struggle to fit either in half a day door to door. I would opt for Hampton Court and it's also on a direct train route.