Front squats will cause more quadriceps activation than a back squat when weights are the same, so they’re best used to target the quads. The reason is that a front squat forces a much more upright torso position. This torso position requires more quadriceps activation to extend the knees. Keep in mind that this doesn’t mean front squats are bad for the knees – front squats create a more natural squatting position that is very safe for the knees.
Front squats are still a good glute exercise as people can typically sit deeper in a front squat than a back squat. Increasing squat depth is one way to increase glute activation. However, exercises like glute bridges and hip thrusts are better glute choices than front squats.
Further Reading:
Braidot, A. A., Brusa, M. H., Lestussi, F. E., & Parera, G. P. (2007). Biomechanics of front and back squat exercises. In Journal of Physics: Conference Series (Vol. 90, No. 1, p. 012009). IOP Publishing.
Gullett, J. C., Tillman, M. D., Gutierrez, G. M., & Chow, J. W. (2009). A biomechanical comparison of back and front squats in healthy trained individuals. The Journal of Strength & Conditioning Research, 23(1), 284-292.