Hi! I am a huge Rolex fan, so Rolex for sure. The watch company is legendary. The Rolex watch in the photo is classic, sleek, timeless, iconic. If you are looking for a 31 Rolex, the one you have on is perfect. Two-tone, white roman dials, smooth bezel, oyster bracelet... the perfect combo to me. I would prefer YG though, not RG.
I am not a fan of the Cartier, especially the bracelet which looks busy to me (and a bit dated to be frank). It does not have that "clean look" you are after. I too like clean, crisp looking watches (I wear a Rolex stainless Daytona).
On RG, no for me. I think it's a trend, hard to match with other jewelry (unless you have other RG pieces), and also a possible maintenance issue. RG does change color, it takes years though, especially Cartier RG. You can read up Cartier's RG and how some ladies are seeing color change already. Rolex's Everose is not supposed to change color because they use a mix of platinum, but you may get tired of RG so it's still a no for me. YG and stainless/WG are classics. If you like RG, the combo is great. If not, I would get that same watch in YG and stainless.
Just my two cents for some thoughts. Good luck to you and happy birthday!
UPDATE: Since you asked about RG, if you are considering the Rolex only because it's in stock but you don't love it, I would skip. You can always order it. It may take time (Rolex is really backed up now), but you will get the perfect watch. I would not settle for RG if you are hesitating which is sounds like you are since you asked about it. It has to be love at first sight. For me, I would not settle for something just because it's in stock. I would order what I want.