There are many rather obvious differences: case size (5131 is larger) and case style, different font (more traditional font on 5231), Patek Philippe on dial (5231) rather than engraved on the bezel (5131), different minute hand ...
But in the most important feature, the maps are basically the same (at least in terms of continents/countries). Yes, the map on the 5231 appears more detailed and colorful. This can be very deceptive because a publicity image from Patek's website may not be entirely accurate especially in terms of actual colors.
So which do I prefer? Initially I preferred the 5231 - more traditional case and font, Patek Philippe on the dial and beautiful map. But my view may be changing. I think there is a lot to appreciate about 5131: the non faceted case keeps the focus on the dial; the map is not cluttered(?) by "Patek Philippe"; related, the 5131 engraved bezel has its own unique charm; and also has the more interesting and unusual font. For me the only way to know for sure which I prefer, is to see a 5231J in the metal.
Bottom line - I love both!
But, I have one major disappointment regarding 5231J. It is not with the watch, which on its own, is stunningly beautiful and a watch I would be thrilled to own!
My disappointment is with the company. Couldn't they have done something other than basically recreating the exact map of 5131J? How about a scene (city, jungle, lighthouse, anything - or if a map at least something different, eg a map of just the Americas. All these images have historical antecedents in Patek's cloissone history. To just do the same basic map IMHO shows a lack of creativity and daring and is disappointing. So, yes, I would love to own the 5231J, but it could have been unique and visionary. It is an incredible watch and beautiful, but it could have been even more special.
Best, patekova