Both Greg Norman and Butch Harmon have said a short thumb vs a long thumb is a matter of personal preference. Greg Norman had said he prefers a short thumb as he felt it generates more pressure in the middle, ring, and little finger of his left hand, and he felt it resulted in a crisper more compact backswing.

I believe a short thumb vs long thumb may make a difference in how and where your wrist, arm, and shoulder are able to move as well as where pressure is generated in those same areas. There have been people who have won professional golf tournaments using both thumb positions, so I don't believe that either is definitively correct or incorrect. I recommend basing your decision on which is more comfortable to you, and what you are trying to do with your swing. If you are trying to make a more compact swing then the short thumb may assist you in that endeavor.