But Rolexes cost a lot more than Omegas.
Don't get me wrong, I love them both, and Rolex and Omega are traditional rivals. But when it comes to exclusivity, Rolex is way ahead, and always has been. You can see Rolexes for six-figures while I've not seen an Omega for more than 30K or so (at the top end). On a price/value/exclusivity level, Rolex has it hands-down.
Now, there are a handful of more exclusive brands--Patek Philippe being an obvious example, but there are others--but Rolex is higher in that list than Omega. You can pick up a Seamaster for about 4 grand, but a basic Submariner will set you back 10 grand or so, even on the used market. Omega is pretty awesome though--Buzz Aldrin wearing one certainly gives it Bond-level cache!
Sorry, mild watch nerd.
So, I'll admit I am not a watch nerd. I'm also not the biggest Bond fan. And the Corvette comparison may have been undervaluing Rolex a bit. Maybe Ferrari would be a better comparison?
But I have trouble connecting this info back to the original question. Yes, Rolex is more expensive. Yes, Rolex is more famous. Maybe even "better", as I'm definitely not qualified to assess.
But what makes Rolex iconic to James Bond? The Astin Martin isn't the highest end sports car, or the most famous, or the only car Bond drives. But I'd consider it iconic to James Bond. Partly because of the British connection, but at least in part because it's less famous than Rolls Royce or Bently. The fact that it's more unique helps forge the iconic-ness of the connection. Being more well known as a higher end watch makes the Rolex a stock luxury reference for Bond rather than something I associate with the character.