Friction does NOT vary depending upon whether an object is pushed or pulled. The frictional force (static or dynamic) is proportional to the normal force, the force that counteracts and exactly matches the weight of an object that is at rest (or moving at constant velocity). The frictional force will oppose the direction of the force applied to an object to move it. It matters not whether the object is pulled (using a tensile force) or pushed (using a compressive force).