The difference between the two really is splitting hairs. But I'll split a few anyway.
The main pool complex (Grotto, kiddie pool, Cabana cafe) is actually closer to the Dolphin, I think. At least it's closer to the side of the Dolphin that the pools are on - as others have said, it's a hike from the far side of the Dolphin to the pools. (The Swan does have it's own separate pool and poolside cafe apart from the Grotto pool complex).
The Dolphin is physically closer to the Epcot International Gateway, but because of the sidewalks that zigzag in front of the Dolphin around the lake, it's probably faster and easier to walk across to the Swan to the bridge. Thus, for walking to Epcot, the Swan is just as close or closer. (And it's faster, and less distance, I think to walk around the BC/YC side of the lagoon than through the Boardwalk to get to Epcot.
I prefer the rooms in the Swan over the Dolphin, though I prefer the amenities of the Dolphin (Tubbi's, the Soda Fountain). I believe the beds are the same, which is a bit odd, since the Dolphin is a Sheraton. But the website mentions Heavenly Beds for the Dolphin, not Sheraton Sweet Sleepers. I usually stay at Westins, but was at the Dolphin two weeks ago, and couldn't tell the difference.