Personally I'd do nonstop though indeed, TP-wise, you'll double your intake via the US. JFK-GIG is a route I had to fly a few times in the last two years and I had the old 777-200 substituted two out of three times and that was not a pleasant experience. I think it is seen as a predominantly leisure route so gets more subs than JFK-EZE (on which I always had the new cabins). Also, the US remains one of the worst countries to internationally transit at for obvious reasons. Finally, you double your travel time and I'd much rather spend the extra time in wonderful Rio if it means I can have half a day free instead of it being only work.