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.
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.