Both are very nice hotels on Disney property, however they are owned by Starwood not Disney. The Swan is a Westin while the Dolphin is a Sheraton, so I would imagine the Swan is a little bit nicer. They do a lot of conventions and are the business hotels of Disney. The restaurants in these hotels are also nicer than most of the Disney restaurants which have gone down in quality dramatically to support the Disney Dinning Plan. If I was going on vacation to Disney the swan or dolphin would be at the top of my list.
Dolphin is the hotel with the large convention space. It has a larger lobby. It is usually crowded when there is a convention going on.Both have good places to eat but they are pricey. I would stay at the Swan.The walk to Epcot or The Studios is a little shorter if you stay at the Swan. They share the same boat dock to Epcot or the Studios but are 2 different stops if you are taking the bus to and from MK AK or DtD
The rooms are not necessarily different, the lobby s differ, but the distance to Epcot, the boardwalk and the boat dock are the same. So I would just go for the cheapest offer.
Never stayed at the Swan, but ive stayed at Dolphin. And it was really nice