We split our trip a year ago and although we liked both everyone in my family voted to return to the AKL this year. The reasons were:
1. The AKL was much quieter, the main building at the Poly felt like Grand Central Station.
2. The kids liked the kids club at the AKL better.
3. The pool at AKL was much warmer than the main pool at the Poly, and it had hot tubs.
4. We liked Boma better than O'Hana.
5. Animals! (from the 8-year-old).
6. Easier to navigate (kept getting lost on the winding paths of the Poly, but we have no sense of direction).
You really can't go wrong with either resort, both have lots of positive qualities so it really boils down to what theme and layout appeals to you most.