I'd love to see your old gold Rolex! I think they're very charming.
As to the original question, I like date on my watch so that rules out Cartier (unless you get it in bigger sizes, which I also don't recommend for daily wear due to comfort). I also prefer round faces for easier reading, and mechanical movements for a bit of 'soul'. So that would tick all Rolex for me.
Your personal preference and style will vary, so there's no right or wrong answer. How do they make you feel? You're not getting a watch for the most accurate time-keeping (otherwise go for digital with atomic time sync function...), but a whimsical wrist companion. They are both timeless, classic pieces but really quite different.
I think Cartier places looks first while Rolex has a form-follows-function design aesthetic. So honestly, I think Cartier looks more elegant on the wrist, but Rolex is just a bigger joy to wear and interact with on a personal level.
And while Cartier does have an impressive horological history, they're much more spread out over a variety of endeavors. Rolex is ultra-focused on JUST watches, keeping a tight lineup and constantly updating them with small but important improvements. I would trust the Rolex to last much longer than Cartier under similar conditions, if that matters to you.
In the end they're both really nice watches so just get what you love on your wrist (be sure to try it on--no amount of internet opinions can replace that)!