more weight always equals more strength
In terms of weight training, the amount of weight (or load) is directly related to strength gains. In fact the only way to make strength gains in the weight room is to consistently lift within 15-20% of your 1-repetition maximum.
Most athletes will have a heavier back squat compared to their front squat, this is because the back squat recruits more muscle groups (glutes, hamstrings, quads, lower back) than the front squat, which like you said is primarily a quad exercise. Because you can handle more total weight with the back squat, this makes it a better lift for overall strength, the front squat would be used to target the quads at knee extension.