Fat doesn't add structure/crispiness to cookies. Fat, regardless of the application, get's in the way of protein fibers attempting to bond and creates tenderness. The more fat, the less structural integrity there will be in the finished product.

The differences caused by sugar in these two scenarios relates to quantity. Small amounts of sugar in bread will, just like fat, get in the way of protein fibers and create tenderness. Once you hit the quantity of sugar in cookies, though, the sugar takes on a structure of it's own and provides chewiness/crispiness.

In what way are your rolls not hard enough? Is the crumb too squishy? The crust not crispy? The crust not chewy?

You may not be backing off on the fat/sugar enough. You also might be underdeveloping the gluten by insufficient kneading. What recipe are you using? You also might be using flour that isn't strong enough. Try a higher protein flour.