I happen to prefer the case of the 513x over the 523x. Generally I not a huge fan of flat bezels and I really like how the 513x wears on my wrist. It is less in-your-face elegant in my opinion. I like to dress down mine with a calf strap and find it becomes quite casual. I also like the absence of a logo on the dial even though I am not the biggest fan of the engraved logo on the bezel (but given how discreet it is I am happy to let it pass)...
I do very much agree on the wish for something else on the enamel
dial. Same map seem a very weird thing to do by Patek... anything else has been better in my opinion...
Would I prefer one over the other? Personally I am somewhat biased but I do like the 513x a bit more overall but both are gorgeous timepieces! 