The Swan has the first pick up and drop off for buses. The Swan has 2 queen beds and a nicer bathroom area, IMO. The Swan has a smaller footprint so that rooms are never very far away from the elevator, lobby, restaurants, etc. The Swan is closer to the Boardwalk (just walk across the bridge and you are there).
The Dolphin has a much larger lobby with more amenities than the Swan. There are restaurants at both hotels, but we prefer the ones at the Dolphin. The Dolphin has rooms that are a bookable category to watch the Epcot fireworks. The Dolphin has a great guest laundry downstairs. The Dolphin has Picabou (cafeteria style quick service and some grab and go items).
Overall, while there are different advantages to both, I just book whichever has availability or a lower price.
Both are great resorts!