Personally, I never quite understood why many people could prefer a 5970 over a 3970.... The dial of the 5970 might feel a bit „bloated“ if compared to the 3970. It might feel a bit like they tried hard to enlarge it beyond its natural proportions (which they did, kind of, of course). Also, the smaller case visually concentrates the mechanics and the beautiful dial in case of 3970.
Furthermore, 3970 was the original. 5970 just a later facelift.
If you don‘t need a larger case because of massive wrists the 3970 seems the better choice to me...
P.S.: a 3970p with black stick dial (total should be less than 150 pieces) is also about 5x as rare as a 5970p (total close to 800 pieces)...