[rwh]

One reason you see fewer cross handed putters on tour is that the players likely to try it have moved on to the claw and its variations.

One perceived advantage is that it tends to level the shoulders and make it easier to set up square. Some players struggling with getting shoulders square will set up cross handed and then move hands to normal without moving the shoulders.

(bold added by rwh)

Good point. I like level shoulders and accomplish that by having both hands side by side on the grip -- what I call my "prayer" grip. The new, wide putter grips (e.g., 2 Thumb ) allow you to keep the hands side by side, but you can do the same thing with a normal grip. I lose the feel of the clubhead with the wide putter grip. I suppose I could add weight to the clubhead, but I like the setup I've got now.