Both trucks require the same amount of work to stop. The Physics Classroom defines momentum as "mass in motion." This means that momentum is determined by two variables; mass and velocity. The work, or force, needed to overcome momentum is described by Newton's Second Law of Motion: F = ma.
The force required to act on a moving object is contingent on that object's momentum alone. A light truck has less mass than a heavy truck, so it must move faster to achieve the same momentum. The extra energy required to accelerate the light truck must be given back when force is applied to stop it. This makes the force required to act on two objects with the same momentum equal.