I thought Breguet was the first wristwatch, but admit my memory is fuzzy on this. Regardless of the accolades of either Rolex or Cartier, I don’t think either is thought of when considering the art of watchmaking. DH’s Alanges outshine both, as well as Breguet, IWC, and JLC. JLC used to provide movements for many watch brands, and their workmanship is highly respected.
i do think the Cartier pasha C is a bit less flashy or recognizable than a popular Rolex GMT or Submariner, but only a bit.
If you define luxury as less mainstream, more artisanal, more high art horology, neither Rolex nor Cartier (at least the popular models seen on TPF and IRL) might qualify. I’m not saying this to bash either brand; I love the Cartier and Rolex watches that I own.