The Enterprise didn't move along with the warship because of inertia (i.e. "a body at rest tends to stay at rest"). When the warship reversed thrusters and pulled away, the inertia of the massive Enterprise acted as the opposing force, and the difference between these forces overcame the friction from the twisted, entangling wreckage and allowed the ships to separate.
Ships do have inertial dampers, but these force fields act primarily on objects within the ship (notably, the crew) to keep them from experiencing the effects of extreme accelerations. Inertial dampening fields, as I understand it, don't actually reduce the inertia of the ship itself. Instead, structural integrity fields are used to increase the effective strength of the materials in the hull so they can resist the effects of extreme stresses. Therefore, the full 3.25 million metric tons of Enterprise-E made for a rather significant inertial force resisting the pull of the reversing warbird.
EDIT : To explain with a simpler example, you can consider this example of inertia, in which a heavy object is supported by string A and has another string B hanging below it. If you pull slowly on string B, string A will snap first because the weight of the object combined with the pulling force stress string A more. However, if you pull hard on string B, the inertia of the heavy object resists the sudden movement and causes higher stresses on string B, snapping it first.
The full-power reverse of the warship thrusters is equivalent to a sharp tug on string B, string B is equivalent to the wreckage holding the ships together, and the heavy mass is the Enterprise.