There are two main properties of a large foil kite that factor into its performance - inherent stability, and controllable stability.
Inherent stability is exemplified by the rider moving along with a kite fixed in the window. As the kite passes into turbulent wind, an inherently stable kite will get knocked around, but recover mostly without any rider input. Many kites like the HQ "Matrixx 2", Pansh "A15", and the Flysurfer "Speed" series.
The problem with inherent stability is that it tends to limit 'controllable stability'. This means that with the kite being somewhat self responsive, rider inputs are dampened. Thus there are effectively less controls available, or those controls are limited in range. Also, inherently stable kites tend to sit further back in the wind window, making them less capable of upwind angles.
Controllable stability is exemplified by the rider, once again, moving along with a kite fixed in the window. As the kite passes into turbulent wind, the kite will catastrophically fail (crash) without the correct rider inputs. However, by giving up a bit of inherent stability for controllable stability, there are more options available if the rider is skilled enough to understand/feel them.
Turning speed, and stall capability, are primary rider inputs which a controlably stable kite has. Oversheeting in an updraft (horizontal or vertical) can stop the kite from overflying the window (though it is counter intuitive). A quick turn can also set the kite back or gain valuable altitude to at the kite . Thq rider can also quickly turn upwind or downwind to change or set up a different apparent wind window position. Kites that have these properties are the HQ "Matrixx 1", Ozone "Chorno 2" and to some degree the Flysurfer "Soul" and "Sonic" series.
The big takeaway from this explanation has to do with rider experience. It takes lots of light wind flying time to understand "controllable stability" to the point where you can use it. An inherently stable foil kite.... well you could teach a monkey, or even someone who has only flown inflatables, to use it.