What sport is the athlete participating in?
In any case, obviously, Front Squats and Back Squats are done for Strength, (please do NOT use them for purposes of conditioning…there are FAR better and LESS riskier ways to conditioning).
Front Squats will concentrate more on the Quadriceps. Back Squats concentrate more on the Posterior Chain (Hamstrings, Glutes, Lower Back).
If we take an example of a track athlete, most of their workouts use the quads predominantly. The posterior chain muscles lag behind in strength development, usually. This is ok until the athlete tries to stretch their own limits (as they would, during competition and when they are trying to improve on their Personal Best during practice). There comes a point when the hamstrings for instance are not able to keep up with the quads and injuries (such as tears) to the hamstring happen. These could be quite severe, keeping the athlete out of practice for a long periods.
Considering athletes such as in the sport of Olympic Weightlifting, here too, the Clean and Jerk, and the Snatch, all involve a lot of Quad involvement. Even so, these athletes need to Front Squat and Back Squat, as part of getting strong.
Back Squats are very good (as are Front Squats) for non-athletes too. With a strong posterior chain, everyone benefits. Injuries such as the very commonly occurring Lower Back pain can be minimized/eliminated.
There are variations associated with the Back Squat too (High Bar, Low Bar…), and many debates about which ones are appropriate under various circumstances. However, for the most part, working out with Back Squats, with some Front Squats thrown in too, are perhaps, the most beneficial to athletes, across ALL sports.
To state the obvious, Strength Training involves more than just Back Squats and Front Squats. Also, all workouts need to be performed as part of a personalized and well thought out training regimen.