.....each of those watches are so different that it really is like comparing different references across all. I think all of them are extremely special. If you asked which would I like most for myself if i was only allowed one, then it would be the 5131P.
There is one thing that I don't like the bracelet is his buckle. A little difficult to use. I prefer Rolex buckle. Overall 5131/1P looks quite nice to me.
... I wouldn't have the 5131-1/P-001 any other way. Except for my wife's various 24/7's and my Nautilus pieces the only other Patek Philippe watch I have with a bracelet is 5180/1G-001. I don't really know but it seems like the designers put a lot of thought into the question of strap vs. bracelet and for the most part I think they get the answer right.
I think PP designer made a right decision to choose bracelet instead of leather strap. Bracelet is very useful and unique. This makes 5131/1P very different from other 5131 models.
All of the above are very special in their own ways. The 5131/1P is quite different with the portrayal of the Arctic polar cap. The 5131R has a special warmth to it with the Pacific Ocean dividing Asia/Australia from the Americas.