When a small lab cart collide with a large mass then during the collision two bodies will remain in contact and then apply the contact force on each other
This contact force is always equal on two bodies in magnitude and also it is normal or perpendicular to the contact surface.
This will always follow Newton's III law as per which every action has equal and opposite reaction.
So this contact force will not depend on the mass or any other factor but it will remain same on two colliding bodies.
So here the correct answer would be
They both experience the same magnitude of the collision force.