This is from my experience on the road course wider tire get better grip than the narrower tire. See most of the race car use the wider tires. It is also depend on condition of the track. If the track is wet the tire with many grove will prevent hydroplane better than small grove. Because when driving on the wet road the water get between tire and road but many (wider) grove let the water escape from the tire so the tire have more contact surface to the road.
Rally car use narrower tire on the snow road, also on the muddy road rally guys use wider and deeper grove.