The best squat style for developing bigger quads is the upright close stance high bar squat in weightlifting shoes. This version forces the quads to perform a lot of work and allows you to lift heavy weights
Why the high bar squat?
The high bar squat calls for an upright posture. This alignment keeps the pressure on the quadriceps. Conversely, the classic low bar squat forces you to bend over more and makes the posterior chain muscles (hamstrings and glutes) even more involved in the squat. In simple terms, the low bar robs the quads and gives to the posterior chain.
Why not the front squat? You could be even more upright.
Because the front squat is not comfortable for high repetition work and does not allow you to lift as much weight as the high bar back squat. Of course, the front squat will develop your quadriceps too, but it’s not as optimal as the back squat. Furthermore, the front squat places more stress on the knees which can be an issue if you increase your workload.
Why close stance?
The close stance is the best for quads because it reduces the involvement of the inner thigh muscles (e.g., adductors).
Why weightlifting shoes?
Weightlifting shoes allow you to stay even more upright. This increases the stress on the quadriceps even further. Moreover, the wooden heel of the weightlifting shoe helps you squat deeper. The negative side is that weightlifting shoes stress the knees more.
What about sissy squats?
Sissy squats place too much stress on the knee joint.
Why not hack squats?
The hack squat is a decent quadriceps exercise, but similarly to the sissy squat, it’s notorious for killing knee joints. Most people will experience problems from hacks squats in the long run.