The tyres make a lot of difference in road holding in cross winds. Supposing that you drove both cars on the same road and in the same direction, and with the same cross wind speed and attack angle, the only parameter left is the make and type of tyres.
However, it seems to me that all the previous parameters being very similar, would be one in a million chance.
AFAIK, 5-door and type-s are the same height (1460 mm) so it means that the type-s is not lower and thus more stable due to that. It may only be due to stiffer suspension and anti-roll bar.
Personally, (mine is 5-door 1.
I've been through cross-winds at about 50-60 km/h recently, and the car surely feels it, but not trying to change lanes instantly. I did not feel any discomfort when traveling at 110 km/h. BTW, I have 205/55/16 winter tyres currently installed, which are inferior to the original 225/45/17 in terms of lateral stability.