Considering the ages of the kids, my vote is the Dolphin. We have stayed at both PO-FQ and the Dolphin, and my kids (ages 10 and 12) prefer the Dolphin hands down!
They love the close proximity (walking distance) to EPCOT and STUDIOS. Very convenient for those rushes to TT, TOT, and RRC!
They also love walking over to the Boardwalk in the evenings for all the action there.
And the Grotto pool area at the Dolphin is probably second only to Stormalong Bay! They love the waterfall, spring pool, and the three hot tubs at the Grotto.
Rooms are bigger and therefor more comfortable at the Dolphin. The layout is nice, with an extra dressing vanity outside the bathroom. Also, the Dolphin is generous with complimentary upgrades if available (just ask!) - Love the balconies!