I don't know if I am the master since I haven't box squatted in 4 months. I do miss it very much however.
The box squat(or bench squat) is superior in my mind because you can teach someone how to squat correctly in a matter of minutes. It offers several advantages.
1. Once you set your box height, you always squat at the same height. Athletes almost always squat higher as the weight gets heavier. This problem is solved with the box. If an athlete squats 1000 times they will squat parallel 1000 times. How many times do they get parallel with a free squat?
2. The coach can dictate how far he wants them to squat. If you want parallel squats you can set the box there. If you want more of an olympic squat, you can move it down.
3. Because you pause on the box, you have to overcome inertia at the bottom. This creates starting strength.
4. You are able to sit back further than with a regular back squat. This causes more hip and hamstring involvement and takes stress off of the knees.
5. If you squat correctly on a box, you can squat easily without it. However if you squat wrong on a box, your free squat form will be terrible.
6. Westside claims that you can recover faster from a box squat. I have no idea if this is true but Louie Simmons has forgotten more than I will ever know so I will take his word for it.
I prefer it the most for reason #1. When working with large groups, it is much easier to have them squat on a box so you know they aren't doing the hillbilly dance.
Guidelines with the box squat.
1. You do not crash on the box.
2. You do not relax on the box. You pause but you must stay tight.
3. Only move the box height down once your athlete has mastered the technique at a higher box. Start high and then move down.
4. As with all squats, the butt should move back first, then the knees should bend.
5. This is not the BFS box squat. Less weight is actually used because the box is close to or at parallel and you pause. You should squat 50+ lbs. more than you box squat if, and only if, you do it correctly. My best meet squat was about 200lbs. more than my best box squat. Some of that weight is due to my squat suit straps being up though. But I could always expect at least 100lbs.