It's a difficult one to answer. On the surface, POFQ 's Doubloon Lagoon looks a more of a "fun" place with the fantastic sea serpent slide and the really cute alligator figures which may be more than enough to attract the kids.
However, apart from those details the pool at Ol' man Island is probably overall better. It's more secluded (and not overlooked by accommodation buildings) has lots more subtle detailing and some great waterfall features, it has a much longer slide (which is often overlooked because it's less visible), and the pool bar and hot tub are both within better sight-line of the main pool if you've got kids you need to watch over. It's also worth remembering that POR has five quiet pools too, which may suit less adventurous swimmers better.
But as has been said, you can pool-hop anyway so try them all!
Andre