I've stayed at both places and like them both, though I prefer Kitty's (the three beachfront cottages) for its beautiful beach, convenience to Placencia village and the lower peninsula and great laid-back Belizean atmosphere. Green Parrot is up in Maya Beach and is an expensive taxi ride back and forth to Placencia village, the airstrip, etc.
Both are now open following Iris.
Neither Kitty's or Green Parrot has air-con. You don't really need it if you are staying on the water and if your unit catches the breeze, which is the case with both of these.
Mosquitoes are rarely a problem on the water when the breeze is blowing, which is most of the time. Sandflies are sometimes a nuisance but they are not terrible here.
Both places have pretty good restaurants. There are a number of other restaurants up and down the peninsula (though some have not yet reopened) so you will probably want to eat at a variety of places.
Green Parrot was sold a couple of years ago, and that has improved it. Kitty's has been for sale, almost sold a few months ago, but the sale fell through.
Belize First www.belizefirst.com/