Box squats and free squats debate again…
they are two completely different exercises. Some people can box squat more than others, some people are better at the free squats, depends on a lot of factors.
Depths, techniques, stance, where you place your bar on the back, whether you are rocking or pausing on the box etc are just some of the factors. Switch them up every once in a while, theres no “best exercise”. You can use both for explosive movements or ME movements.
However, a lot of coaches like Cressey and Mike Boyle eliminated free back squats for their athletes in favor of low box squats and front squats. The reason for this is because you can get the same benefit/result with front squat, and it is more “sport specific” (if that term even exist) and you cant cheat on it like the back squat where some people lean forward with it or good morning it up with heavier weights.
Box squats also put less stress on your knees and back since your knees don’t pass shins. You can also recovery faster with box squats.
Remember your body only knows stress and adaptation. As long as you are giving your body more loads/stress and allow it to adapt you will get stronger, it isn’t going to pick one exercise over another.
ps. if you squat to 90 degrees or a quarter, you will not notice gains in the full squats, but full squats do have a good carry over to half and quarter squats.