I do think there’s something to the tech when it comes to handling cross winds; the 42mm deep OEM wheels I had on my TCR were pretty twitchy in cross winds, where as the 37mm Bontragers I have now are very well behaved. In fact, they are noticeably better in that respect than the 33mm Hunts I had before them. So there is IMO more to it than just depth.
There are plenty of detailed reviews out there, so I’d do some research if cross-wind performance is a real priority/worry.