Without watching you do it, I can't speak with certainty, but, my guess is that you have your feet too close together and you are attempting to quad squat, rather than properly squatting with your hips, hams and glutes.
My knees hardly ever experience any pain whatsoever when squatting on a box. I take a very wide stance and sit back as far as possible, and this seems to take the pressure off my knees.
When you squat, do your knees tend to go in, or out? I bet they are going in and if that is the case, you need to widen your stance and/or actively push your knees out as you stand up off the box.
And regarding the big numbers, get the form down first. Numbers will come. Everyone has to start somewhere. The main thing at this point is to get your form down to perfection. This allows you to get as strong as possible, and it keeps you from getting hurt.
B.