rear tyre is the same profile just wider, will make a bigger difference on corners. 60 is the profile/height from rim to bottom of tyre.
going up in profile would do the same as changing sprockets, i always try get 10 more on the profile if i can, have had wider tyres they do feel like they have more grip on corners but that will be down to the width of them, the cornering will be a bit slower but feel smoother