From what I understand it can be pretty difficult to know what exactly makes different cars feel more sensitive to crosswinds than others so take any general ideas with a grain of salt. There seems to be some truth to the idea that the type of steering can influence negative dynamics of the car in crosswinds, in one research article[1] those drivers who just went along and didn't over-correct ended up moving the car around less. So electrical power steering might be too direct for some drivers and increase the cars movements to the sides especially since the crosswinds usually come in unpredictable short bursts. This could be tested by changing the steering response in the Model S to a less sensitive setting on the touchscreen. The general consensus is that cars with low coefficients of drag are more sensitive to crosswinds because of their asymmetric side surface area but apparently a "Kamm rear end" (Prius) mitigates this.
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However why a car is more or less stable in heavy crosswinds is answered by the fundamental properties of the car: Center of mass, Center of steering forces, Aerodynamic center of pressure, Tires, etc.
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Here is the link to the full [1]
article.