The other over grips I had been trying were too tacky. When I shifted my grip between shots they would not allow the racket to slide around unless I completely released the handle, making it hard to find the new grip. The Tourna grip allows me to slide the grip around rather than break contact. This is why I prefer them.
May have to give the Solinco ones a try, though if they are thicker, that's probably a drawback.