I've stayed at regular Swan and Hilton Bonnet Creek. My thoughts:
A big plus of Swan/Dolphin is that you can walk to 2 theme parks. Usually at a much cheaper price point than the Disney resorts in that area. You also get the advantage of Disney transportation (busses and the boats) and have a lot of food options at your disposal, since the Swan/Dolphin has several, and you can walk to Boardwalk and Yacht/Beach. As others mentioned, you get some of the Disney resort perks as well.
The two big plusses of the Hilton are the price and the pool. The price will likely be half that of the Swan/Dolphin and you can sometimes get extra free nights, depending on your length of stay. And the rooms/beds are nicer than Disney hotels at that price point (though probably equal to Swan). The pool complex at the Hilton is fantastic - a huge lazy river - and it is usually not super busy. You have access to restaurants at Hilton and Waldorf, though Swan has bigger selection. Busses are ok, better than the Disney Springs area offsite hotels, but still not as frequent as Disney proper. I believe they run on a "once an hour" schedule.