Having been bought up near both locales I am really torn. Hampton Court is a must see if you have been watching The Tudors on TV - Henry VIII "took" it from Wolsey, it's haunted by Jane Seymour (the Queen not the Actress). The front part is pure Tudor and the rooms still have the original panelling and Tudor Rose Motifs. The rear was built in the reign of Charles II (I think maybe designed by Wren), and is pure Restoration period decoration and furniture. Visit the kitchens, the "Real Tennis" court, and the lovely gardens.
Windsor Castle is huge. A lot of what you see externally are Victorian renovations, and of course one wing was redone (beautifully) after the fire some years ago. St. Georges Chapel is beautiful and is rich in history as it is the home of the Knights of the Garter and dates back to 1200-something and was renovated in the 1300's. The State Apartments are open to the public. Wonderful views across the Thames valley to Eton amd beyond; well worth walking into Eton to see the college - you can check the College Website for information on costs, times etc.
Windsor town is quite quaint - with a covered market/town hall.