We've stayed at both many, many times. We do prefer the Swan because it is easier to navigate and the atmosphere is a little more intimate.
The biggest difference is the size. The Dolphin is much larger. In certain areas you will need to actually transfer elevators if you want to get to the ground floor to the boat launches. You can also take the escalator from lobby level but this is tough to do if you have a stroller. Bus transportation is picked up on the west side of the resort so if your room is in the east wing it can be a long walk.
My 8 yr old dd loves both but likes the Swan a bit better because it's a shorter walk to the room. She's been spoiled at the S/D since she was 2. There may seem to be more kids at the Dolphin because it is so much larger. But, it really varies.
Another room difference is the sinks. The Swan has 2 sinks, one in the bathroom and one right outside the bathroom. the Dolphin has a vanity area across from the bathroom area, but not an extra sink.
As mentioned there are more amenities available at the Dolphin but they are there for you if you stay at the Swan, you just need to walk across the courtyard area.
mouseRD-we tried Blue Zoo FINALLY for the first time on our past trip, it was excellent!! We also are big fans of the Palio and this is a "must do" every trip!
Oh and one last thing, you might find more info about the S/D on the Disney Resort board. Even though they aren't owned by Disney they are on Disney property so they are considered Disney resorts for that reason.