You probably have a flexibility issue Built, I'm not going to lie. Flexibility is a huge issue in squatting deep while keeping an upright torso - most people just don't have the ankle or hamstring flexibility to do it so they tend to fall forward. Ankle flexibility is a big issue even for people who work on their flexibility because it's often neglected.
And if this is the case, it's no surprise that you remain more upright during low-bar squats. If you're squatting with a high bar placement the lever-arm is going to be longer and, thus, it's going to be tougher to stay upright.
I see this happen with front squats all the time - people's elbows tend to drop, their torso lowers, and they tend to fall forward, sometimes even stepping forward to keep their balance. In the end this is a flexibility issue, but I've found that focusing on keeping my elbows as high as possible (the cue I use for my own training is "elbows towards the ceiling") will lead to an upright torso and a balanced squat with no problems losing the weight forward.
cshea:
In all sports you're going to use your hips and ankles to bend. Box squats are fine but there's not going to be any good to come out of developing strength from the bottom position of a box squat. It's just not a position you will ever encounter in any sport unless you are falling backward. You are confusing a bent-over position with the position involved in box squatting. They are entirely different if you look at pictures.
Look at the angles the shin and hip makes with the torso here:
Now tell me how the shin, hip, and torso relationship here is remotely the same:
The reason I dismiss it as being for geared powerlifters has already been given - strength is specific to positioning. Geared powerlifters find themselves in this position often. Athletes do not. Raw lifters do not. You are working on strength from a position that you will never encounter in your sport. Not only that, but you are working on a position that powerlifters specifically use gear to support and you are a raw lifter.
Every athlete wants to develop hip extension - it's crucial to about every sport. The key is to find the right positions and use your training to strengthen only those. You don't see olympic weightlifters performing low bar box squats yet their sport involves some of the most explosive hip extension you will ever see. The reason for this is simple - they're never in that position in their sport, so why should they train it? There are so many ways to develop hip extension it's not even worth it to list them.
You know what has the best carryover to a free squat? It's free squatting.