When matched properly, wider tyres and wider wheels mean more rubber on the road to increase traction. Following this school of thought, there's a reason cars on the track use extra-wide racing wheels and tires, because they grab onto the road and start moving instead of spinning. The wider tires performed better in the slip-pad test, producing more turning gravity than the thinner tires. When it comes to stopping distance, wider tires usually always reduce speed faster without dramatic effect.
Wider wheels are likely to be heavier. The wider tyres mounted on such wheels also make it easier to follow the ruts in the road - pulling you from side to side if you are not paying attention. Wider tyres do not cut paths in wet or snowy conditions as much as narrower ones, and are more likely to spin and lose grip in heavy rain conditions. Because the wider tire has a larger contact area with the ground, thus has a higher rolling resistance, which will also cause the increase of fuel consumption