The classical back squat and its variant the front squat rank among the most important exercises for strength and general fitness training. But which one is better or might this even be the wrong question?
Back Squat advantages
Back Squats utilize nearly the entire muscular system, however they put the biggest emphasis on the posterior chain (lower back, glutes and hamstrings). Therefore it is a classical leg exercise.
Compared to front squats, back squats are "easier" to learn, since the recruitment patterns are less complicated than the ones of the front squat. Therefore it is one of the first exercises I want my clients to master in order to lay the foundation for a sustainable strength training and body transformation.
Even though the back squat is easier to learn than the front squat, many problems can occur preventing you from being able to squat properly in the beginning. The usual suspects are tight muscles, bad mobility, injuries and other biomechanical disadvantages. However, compared to the front squat the back squat doesn't require a strong upper body and therefore is choice number one for people being new to strength training.
Front Squat advantages
Front squats can be considered to be an advanced exercise which puts more training stress on the whole body and central nervous system and involves the core, upper back and chest to a bigger extent than the back squat. When aiming for developing overall strength and muscular balance it is a more bang-for-your-buck-exercise than the back squat.
Being tougher on the whole body and central nervous system, the front squat usually gets executed with significantly lower weights than the back squat (~15-30% less, if put into numbers). Sounding like a disadvantage this circumstance actually can be beneficial since less weight but more muscle recruitment can improve overall strength development and muscular balance as well as technique and mobility better than higher loads on the classical back squat.
Conclusion
Both exercises have their advantages and the question should not be which one is better but which one should be used when and under which circumstances. As a rule of thumb you should be able to master the back squat as well as the compound pushes and pulls for the upper body before jumping into learning the front squat.