Well today I put on the babolat pro team tacky on my other ps gtl and wow. It was noticeably thinner than the other racquet with the head leather. Now that both have the same over grips, the babolat one feels thinner(sorry had to repeat myself), you have more feeling of the bebbles, and overall seems to grasp better.
So if you go with no overgrip, go with head.
If you put on an overgrip go with babolat.