The golf ball delivers much much greater energy to the guy's head.
Energy delivered to the target matters.
If you don't believe me, you provide the test head and I'll provide the ping pong ball and the golf ball.
"energy transfer" or "energy dump" is BS. Energy is the ability to do work. It does not mean that the work gets done, or that it is the work you intended to do.
Here's another test. Put on a baseball mitt. Catch a baseball. Next, catch a 22 rimfire fired from a handgun. Same amount of energy. The entire energy of the baseball is absorbed. The 22 will likely pass through your hand, and your hand will absorb a small amount of the 22's energy.
Which one did more work? The baseball. It moved your entire hand. Your hand bounced back slowly, absorbing the momentum.
The 22 did less work- it moved a small amount of tissue- very quickly- but only a small amount. But it did more damage.
The amount of energy is only a small factor in the amount of damage done by a bullet. As others have said, there are other factors that are more important. An even bigger part of the picture is whether the damage is effective in stopping a fight and that mostly comes down to placement.