The CP is in a gated plantation and has tons of recreation, huge tennis center next door, and gorgeous landscaping. It does cater to conventioneers, there doesn't seem to be as many families there. You'll need a car or taxi to go to restaurants or shopping outside the plantation. The seafood buffet on the property is both terrific and expensive, even for HHI.
The HI is located within easy walking distance to a good sized shopping and dining area with lots of entertainment as well. The HI caters to more of a family crowd and has a seasonal beach/pool bar as well. Parking is something of a pain, as there is not seemingly enough in the summer. That particular part of the beach just got a lot more crowded in the past couple years due to a new park-like beach access point nearby. (At HHI, the entire beach is public, but access to the beach is only allowed to the public, at least officially, in a few spots.)
PM me if you want more info.