Adam - you should not feel pain in the wrists when back squatting. The weight should be loaded all on the traps. The hands are there to prevent the bar from moving back and forth. You do not attempt to push the weight up with the hands at all.
Squatting low bar is not going to help you squat high bar. Just start squatting high bar and try to get deeper gradually. Get more flexible and mobile. Ankle mobility, hip mobility, thoracic mobility. Stretch those quads, calves, hamstring, glutes and adductors..
In the Clean & Jerk and front squat, the bar is placed across the shoulders and clavicle, just in front of the neck right. The front squat is the main exercise used for squatting for weightlifters because in the clean recovery, you are front squatting the weight up.
Olympic Weightlifters squat with a high bar placement because the bar is closer to the front than a low bar placement. This means it mimics a front squat much more than a low bar squat = more training effect and specific.
The high bar squat and low bar squat are two totally different creatures. However, it is known that the high bar squat requires more flexibility and mobility to squat ATG. This means you will be more flexible and mobile. More practical eh?
Then again, it depends what is your goal? Olympic Weightlifting - high bar. Powerlifting - low bar.
Like what coachdavidh said, the high bar squat stresses more on the quads and less hamstrings. More anterior than posterior. That's why Olympic Weightlifters have big quads as compared to the rest of their body
Google 'Asian squat'.