By first pull, I mean the continuous explosion that starts from the floor (or the hang) right up to the point you drop under the bar. This 'explosion through the hips', even if you want to divide it into two phases, is where the speed strength is developed. The next phase, the front squat, is not explosive, and does little in terms of converting absolute strength to speed or functional strength. And because the weight is much lower than your 1RM for the back squat, there is little gained in terms of absolute or limit strength in the glutes and hams. See somebody Powercleaning 405, they're an animal. See somebody squatting 405, ho hum. My 19 year old nephew can full squat well over 600lbs (did this in a drug free powerlifting contest, setting several records) and can deadlift just under 600. He can't front squat much at all, because he never feels comfortable in the lift. It's d%#@ hard to hold 600 pounds on you collar bones.
I don't believe the front squat is so much indicative of higher leg power as it is indicative of good form, practice and good flexibility. It's an awkward lift. The back squat is the best indicator of Posterior Chain strength, and is, IMHO, the best all around exercise for improving lower body absolute or limit strength.