I haven't personally stayed at either, but my parents and brother live in FL and like to take advantage of their resident rates. They normally pick the Dolphin because of the rates (i.e. they are usually noticeably lower than the Swan), but they seem to prefer the Swan and would choose it first if the rates are close. Here's why...
1. Swan is smaller
2. The Dolphin has the bulk of the convention facilities, so Swan tends to feel less chaotic
3. Swan is Westin and they have AWESOME beds! (Dolphin is Sheraton...not bad beds...but not Heavenly beds)
4. Speaking of beds, I believe there are still some rooms in the Dolphin that have doubles instead of queens
5. My SIL prefers the Swan decor
Now, I've been inside both and both are kind of neat in their own ways. If you happen to get Starwood Resort rewards, you might also look to see if there are any special rates.