A wider nose has more foam which increases the paddling ability and the ability to catch waves. Wider noses are better for smaller surf because the wider nose resists sinking and plowing the water as you move forward. Generally the wider the nose the less nose rocker you want the board to have so you're sure not to plow water and slow down. In bigger surf especially with offshore winds you would want a narrower nose so that the wind doesn't catch under the nose and keep you from being able to drop in.