3970R would be my first choice among the 3 through it aesthetical stand point as I was lucky enough to purchase one years ago before the hype. I sold my 5050J off to get other watches and recently got a 5970WG.
I would rank 3970R before 5970 or 5050 any day but because of its size I don't wear it much as I used to.
So IMO you should get a 3970R and though it looks similar to 5970 yet they are much different as 3970 has that vintage look on it especially in RG.
Since you already have a 5970G which has the same DNA as the 3970 except with some modifications on the dial and the case, the 5050 will bring out a different watch - it's not a perpetual calendar with chronograph like the 5970 and 3970. The 5050 is purely a perpetual calendar with its unique retrograde flyback date hand (it differs from other Pateks like 3940, 5040, 5041, 5038 or 5039). It's also the first contemporary Patek model which has such complication after a lapse of almost 60 years (it followed after the earlier Ref. 96 in the 1930s). The only current model with such complication is 5059. The 5050 can be a daily watch as it's not a thick watch and a classic too. However the 3970 being a chronograph is sportier whereas the 5050 is dressier.

