Both exercises, front and back squats, are as effective in terms of overall muscle recruitment.
The significant difference is that the front squat causes significantly less compressive forces and extensor moments than the back squat.
This result suggest that front squats may be advantageous compared with back squats for individuals with knee problems such as meniscus tears, and for long-term joint health.
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Source: Gullett JC. A biomechanical comparison of back and front squats in healthy trained individuals. J Strength Cond Res. 2009 Jan;23(1):284-92.