When you say the Cook's I assume you are talking about Aitutaki. I've done both, Fiji in 2010 and Aitutaki last year and I'm returning back to Aitutaki this year. IMO they are two different places that offer a kiting experience but it's hard to compare them. Fiji is a lot bigger than both Aitutaki & Rarotonga and probaly offers more accommodations options.
I stayed and Kited around Nananu-l-Ra Resort in Fiji and enjoyed it as my first island kiting trip but I prefer the kiting spots in Aitutaki. If you are comparing these two then IMO the Aitutaki kiting areas around Honeymoon Island & 1 Foot Island are better for flat water kiting and suit most wind directions.
It is just one huge lagoon with a large amount of flat water thats waist deep and for the most has a sandy bottom.
Honeymoon ls has a great little hut on it so as you can come in land your kite and have something to drink, grab fresh fish of the BBQ or jump in a hammock for a rest before heading back out for another kite.
A lot of the better kiting/flatter water in Fiji is done out on the outer reefs and requires you to launch you kite from the boat which is not hard if your lines are set up correctly, get that wrong and your stuck sitting in the boat while everyone else is out kiting.
I found that Aitutaki had More options for a drink or a meal, from beach huts serving fresh seafood right up to 5 star restaurants and I wasn't tied into the one place and the same group of people each night.
On Aitutaki you have mopeds to get around on the island.
Both places have great trade winds
The Cooks will cost you more and things like boat transfers are not included in the costs but its still not that expensive.
At the end of the day they both offer a kiting experience in warm water and trade winds while the rest of us sit here in the cold. PM if you want more details