Are wider tires better than narrow tires?

Wider tires give better traction, esp in less than perfect conditions.

Narrow tires would give better speed and/or gas mileage.

One might think that but not necessarily, it depends on the road surface. Why do ice skates have thin blades? What do you think a wide racing tire would do on a flooded street? Even in dry conditions, a wider tire won't change your traction because even if you have more area (square inches) on the ground, you have less weight per square inch so traction remains the same. How soft the tire is is the biggest factor.