I think you've got the wrong analogy, if that's the right term here.
My impression of an equivalent anterior chain exercise to the GHD for the posterior chain would be something along the lines of:
Imagine a flat or decline bench with roller pads in front of the shin. Subject lies on bench in the normal supine fashion. Subject then raises his entire body (straight or nearly straight from knees to head, knees begin at a 90 degree or less angle) around the pivot point of the knee to a standing position (the feet would likely be against the front roller pad and the floor the entire movement).
Sounds hard to me, and would likely be brutal on the knees (assuming one could even lift off!). It would also stress the hips and quads at the same time, unlike the knee extension machine. The shear force from the thigh pad of the knee extension machine would also be gone, as the thighs would be in the air most of the movement.
The mechanical disadvantage of the quads in the movement I described would appear to be pretty outrageous.