To answer your question directly, ‘sissy’ squats are biomechanically similar to leg extensions, but not entirely interchangeable. So before explaining how and why, it is fair to say yes, there is reasonable justification to employ both in a given micro- or mesocycle. It is, of course, a matter of judgement to decide whether such a justification is adequate.
It is important to emphasise that this analysis is entirely specific to the variation of ‘sissy’ squats that you have linked above. There are other variations to which this analysis can not be applied.
At the bottom position of both movements, the femur is perpendicular (at 90°) to the tibia, and three external forces act upon the system. In the ‘sissy’ squat, the load (the weight of the torso) acts vertically downwards at the proximal end of the femur, and is counterbalanced by a perpendicular reaction force at the distal end of the tibia. A second equal-and-opposite reaction force acts at the proximal end of the tibia, creating a force couple. In the leg extension, the system is essentially mirrored. The load (the weight applied to the swinging arm) acts perpendicularly at the distal end of the tibia, and is counterbalanced by the weight of the torso—plus a reaction force if the athlete is holding the handles—acting at the proximal end of the femur. A second equal-and-opposite reaction force acts at the distal end of the femur, again creating a force couple.
Therefore, the ‘sissy’ squat and leg extension are biomechanically indistinguishable in the bottom position. Assuming that the loads are equivalent, muscular, longitudinal, and sheer forces can be assumed to be identical.
And at the top position of both movements, the femur and tibia are in line (at 180°). However, the forces acting on the two systems are now different. In the ‘sissy’ squat, the load (the weight of the torso) acts longitudinally through the femur and tibia. The two reaction forces are reduced to a small force component, which is a function of the angle of the body created by the two supports. In the leg extension, by contrast, the load and first reaction remain unchanged, while the second reaction becomes the sum of the other two forces.
Thus, in the top position of the ‘sissy’ squat, muscular, longitudinal, and sheer forces are negligible, while in the leg extension, those forces are maximal! Hip extension in the ‘sissy’ squat primarily functions to balance the body: the motion could theoretically be performed without the existence of the hip flexors and extensors entirely. In practice, they are postural muscles.
This, of course, is what we might expect: machines like the leg extension are designed specifically to isolate a joint, and typically to ensure isotonic or isokinetic continuity. Whilst the ‘sissy’ squat is a contrived exercise constrained by an apparatus, it still preserves at least some semblance of natural mechanics.
It should also be noted, finally, that Smith machine feet-forward squats are, from a biomechanical perspective, even further removed from these two exercises. But that will have to be a discussion for another day.
I hope that helps.