Both models are really nicely executed & evolution of the original design with added exclusivity of their new in house movements.
IMO if you want something more sporty & classic Patek style (and I am not talking boring base yet again ;-) ) I would say 5980/1. With the new self-winding, column-wheel-controlled caliber 28-250 C chronograph movement & that "One-Eye" design from the 5960p will be a classic IMO.
Now I know you like exclusivity, but if you also would like "a bit" complications (subsidiary seconds dial at 4 oclock, a power-reserve indicator between 10 and 11 o'clock, and an analog date at 7 oclock with an integrated moon-phase display from the 5055/5085) on a "sports watch" all packed up in a truly different then seen before design placement then 5712/1A is the one for you.
5912/1 If I would be the one to choose it would depend also on what I want this watch to represent. For the sporty choice in the spirit of Nautilus I would have to go with 5980/1. On the other hand if this would be my first & only Patek (quite possible with the favorable larger case size & sportier less stodgier attitude) I would go with the more complicated 5712G - Yes the white gold version :-) Why? Well spending all that dosh I might as well go with the best plus having a precious material Patek with quite daring design needs to be worn on a strap (which I prefer anyways).
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