In a contest, I would take the loaded pistol squat over the back squat any day.
It’s not just because the pistol requires more balance and hip control. It’s not because you don’t need a squat rack, barbell and lots of extra weight. And it’s not just because people stop and stare when I do them in the gym.
It’s mostly because the loaded pistol squat gives you the ability to change the resistance of the exercise without changing the weight. This means you can make the exercise easier and harder depending on the set, the rep and even part of the rep. So if you’re weaker at the bottom of the squat you can make it easier and harder at the top where you’re stronger.
This video explains how: