Putting requires feel for to roll the ball the correct distance, and control to roll it on the proper line. The grip on your putter can influence both. If you're struggling on the greens, you may want to investigate a change in grips. Thicker grips might increase your control, while thinner grips could boost your feel.
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Thick Equals Steady
According to Brad Faxon, a PGA Tour pro famous for his putting ability, thick grips help keep your hands quiet during the stroke. You may find it easier to keep your hands ahead the putter head through the strokes with thicker grips because you'll be forced to swing with your arms and shoulders. That will help you keep the putter head moving low and close to the green, which should make your putting game more consistent. The added control does come at a cost. As of 2013, thick grips were more expensive than conventional or thin grips.
Thin Equals Control
Dave Stockton, a former major championship winner and respected putting coach, believes players should use thin grips. He thinks they make it easier to grip the club in the fingers. He teaches players to use the feel in their hands and wrists to control the pace of their strokes and the speed they roll the ball. Stockton often draws and analogy between holding a putter and taking a coin from your pocket. Both are done with the feel in your fingertips.