Like skiing, it depends on what you're doing when you kite.
For kiting frozen lakes I run a standard alpine setup since no touring mode is necessary, cheap and reliable. I do prefer a rockered, Vibram soled AT boot for running lines and helping others launch kites. Boots are lighter, warmer and more comfortable to be in all day. I use a Scarpa Maestrale RS and Salomon Warden bindings that have sliding AFD's and greater toe height adjust for the rockered sole.
For line of sight roadside accessed backcountry kiting, much like sidecountry skiing I run a Baron touring setup. Nice step-in convenience and the ability to skin back if necessary without too much weight penalty. Haven't had any reliability issues although they do have a reputation for not being as robust as an alpine binding as well developing slop with hard use, although they're supposedly better than the Fritschi frame bindings in that regard.
For longer tour access tech is the way to go. Lighter overall, better pivot placement and not lifting the binding frame with each step is a real advantage. I have an older set of Dynafit Verticals and first gen Fritschi Vipecs. Both tour great. For the kiting part I can manage to pre-release from the Dynafits on occasion on hard jump landings as they're pretty rigid. The Vipecs have a spring loaded heel like an alpine binding and can compensate for the flexing of the ski, no pre-releases and I run 2 points lower on the release value. The newer tech bindings like the Kingpins, Radical 2, Vipec & G3 Ion are pretty robust and have typically have some active heel compensation for ski flex. If I were to buy today I'd get the Kingpin 13, no pins in the heel, aggressive toe retention with 6 springs up front for the pincers and DIN release. This would be a good do it all sidecountry/backcountry setup.
Thanks for all the info. At the moment I ski with Movement Jams with alpine bindings (z12s) and Icelantic Shamans with Alpine Trekkers and skins for short hikes. Both cambered and short radius maybe not the best with a kite? Living in the UK means flying to the snow. So ideally I'm looking for a one ski quiver to ski piste and powder and kite as we need to avoid traveling with tons of gear. I've got lots to thinks about and the Kinpins sound pretty good or maybe F 12 tours with a 100-110 directional rockered ski- I've just seen some 117 Atomic automatics and Guardian 13s on eBay - heavy but good for everything apart from hard pack?
In terms of side cut and a kite the less the better. As edging against the kite cause the ski to carve upwind. But it comes down to how you edge and the surface. On hard/firm surfaces the less the better and longer carve radius is better. On the softer stuff and especially in powder, side cut is less of an issue as you are able to plane the ski vs. Driving the metal edges. Especially if you run a flatter ski. The Automatic is a good ski and can get by on the firm stuff though not ideal. Lately I've been using Dynastar Chams 107 as my all rounder. 190cm rocketed tip flat tail. 21m+ carve radius. It's the closest replacement to my Rossignol Phantom 108s.