It's possible to build a board with similar characteristics with either fibreglass or carbon. These days there's not much cost difference either, so pick a board with characteristics that suit your style, and don't worry too much about core or reinforcement material.
For example, with a foam core, you can get similar flex characteristics to glass by making the board thinner and using carbon. You use less core material, less carbon and less resin, which saves cost.
With foam cores, Airex is a linear PVC, which is tougher than cross-lined PVC (divinycell), but it's not as rigid, so you need to use a heavier density. Corecell is SAN based, which combines the best of linear and cross-linked PVC, but it's double the cost.
Foam cores need more reinforcement than wood cores, because wood cores are inherently more stiff. So you use more reinforcement and resin for foam core boards, which are generally lighter than wood cores.
Wood cores are cheaper than structural foam, but more difficult to work with. Unless you can CnC them, in which case they become cheap again (low labor cost). Wood cores need less reinforcement and less resin than foam cores, which once again makes them cheaper. But they are slightly heavier.
Most kiteboard decks are between 2kg and 3kg. Add fins, handle, wet footpads and straps, and the weight goes up to 4kg or 5kg. Add a grind base or more reinforcement for wakestyle boards, and the weight goes up a bit more.
A 4kg/5kg total weight for a kiteboard is perfectly acceptable. In fact, I don't know how many manufacturers even specify the total wet weight, because it's really not that material. Yes, you can get lighter boards, and yes you may notice a slight difference, but it's minimal and you would probably sacrifice robustness for the sake of a few grams.