Not just "wider tires" like some likes to ridicule. 35mm wouldn't change much indeed. Very much wider tires -> 50 or 60mm, full mtb but without profile, as it is inefficient on slick roads. You keep the geometry. You also impose gum material and an anti flat layer.
Comments
1) much slower, at last
2) better cornering -> again more security
3) punctures made nearly inexistent -> less car support, again better security
4) more comfort for riders
Cons:
1) Advantage other riders, typically heavier rouleurs, Ganna-style, as you impose a base power load