Hi eddiewells! First off, you DO NOT have to have an AP to receive the Teacher's discount, but you do have to be a teacher!
Having stayed at both now, I can honestly say I prefer the Dolphin. Why? Several reasons, but I think it's a personal preference thing. The Swan is smaller, having half the amount of rooms that the Dolphin has, making shorter walks to your room from the elevator. To some people, that is a big deal. To us it's not! You can get just as good views from the Swan as you can the Dolphin, so it's not that one has a better view over the other.
I like the convenience of having Tubbi's Buffeteria just a quick step downstairs, as opposed to walking outside across the courtyard, again, a personal preference! I do think the Dolphin is a little closer to the Grotto Pool, but not by any great distance. The Friendship boat launch to Epcot and MGM is equal distance between the two resorts.
There is just something about walking across the Dolphin lobby when returning from a park or one of the restaurants that grabs me. It's festive, alive and very cheerful. The Swan is very small, but has an elegant feel.
I will say though that I prefer the bathroom set up at the Swan better, but not enough to make me want to switch!
I really thought I'd prefer the Swan over the Dolphin. But the Dolphin won me over for life!
If you are interested, you can read
day one of my trip report which includes a description of our room, and photos of the view from our balcony!