What if any are the advantages of Box Squats versus traditional Back Squats?
What are the pro and cons from a biomechanical, spine safety and athletic performance perspectives?
Depends on your training goal/what sport you play.
Box Squat-
develops posterior chain to a greater degree
develops reactive/starting/explosive strength to a greater degree because of the break between the eccentric/concentric chain static/relaxed overcome by dynamic
is less stressful on the patella tendon
teaches perfect (power) squatting form
is very easy to learn/teach
a big box squat will build a big free back squat, NOT vice versa
is less stressful on the lumbar region of the spine as the pelvis does not exhibit a posterior tilt near (rounding of the lower back) to the degree as it does during a free/full back squat
James
Box squats are more stressful on the hips and the muscles around them while back squats are more stressful on the knees and the quads.
Box squats also kill the abductors 
I could box squat a good % of my free squat the first time I tried em
Don’t do em anymore.
I can also squat up from a dead stop off pins with 90% of my regular fullsquat too. So box squats are not a big deal in this regard
Absolutely right, box squats, IMO, would only be necessary depending on sport and goal, but then again, so does almost every other exercise.
CoolColJ was also correct that, they kill your abductors, which I think is important to consider if you are a hurdler with respect to your trail leg. (this is an assumption since I’m not a hurdler)
I don’t think they’re necessary, although, if I remember right Charlie said deeper squats are useful to activate the upper hamstring more, Charlie?