Will a rough surface have a greater or lesser sliding force and static friction compared to a smooth surface?

Friction is resisting force - a type of force that resists movement. The type of friction that resists movement between two objects in contact with each other is dry friction. There is dry friction between a book and a table, or the wheels of a car and the road.
Dry friction can be divided into two. Objects in contact against each other can be moving with respect to one another or stationary. When the objects are stationary, the friction between them is called static friction. Static friction resists movement. Imagine a box full of books on a floor. Initially, when you try to push the box, you struggle. This is because of the static friction between the box and the floor that resists the force you apply. Overcoming this, it becomes easier. Once the box starts to move, there is sliding friction. Sliding friction is the type of friction between objects moving relative to one another, and always opposes the acting force. Thus, it resists the movement as well as you push the box. 
Friction - whether static or sliding, or any other type of friction - depends on the type of material and the degree of contact between objects. In general, rougher surfaces tend to have higher coefficients of friction - which means they will tend to have higher sliding and static friction. Rough surfaces are surfaces that are highly uneven - maybe because of parts of it sticking out, or just scratched surface. These increases the surface area of contact between two objects, and could contribute to an increase in friction. Imagine the box on a cemented floor. The cemented floor is rough and it will be hard to either start pushing the box or continue pushing it. This is true when compared to pushing the box on an ice rink - where friction is lower and hence, the task is easier.
While this is the general case, it is not always true. For instance, two glasses are very hard to slide against each other. This is because of adhesion between the molecules. There is a point where when two objects are really smooth, friction increases due to adhesion. In general, however, smoother surfaces have less friction, while rough surfaces have greater friction.
http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html