But you are talking specifically about low bar squats - putting the bar higher on the shoulders allows you to keep more upright (in the thoracic spine) like in the front squat. The problem with front squatting (if mass is the goal) is that long sets are not really practical. The shoulders (front deltoids in particular) will fatigue faster than the much larger and more powerful muscle counter-parts in the legs.
If you squat like a powerlifter, the quad involvement is almost none. If you squat like an olympic lifter, quad involvement is much greater.
The powerlifter has the bar low, and therefore sits back into the squat - which causes the shins to stay vertical and minimises knee bend (more stress on the back).
The olympic lifter has the bar high, and therefore (his/her hips) can come down in a much more vertical direction - which causes the knees to bend somewhat (more stress on the knees).
Foot placement and positioning are of course other factors, but the point is that the former variation (said simply) maximises glute/hips/hamstring recruitment, whereas the later (olympic) variation does this but with more stress placed on the quads (due to the greater knee bend)
This is my understanding anyway. I'd be interested to hear other opinions