Both front and back squats can build powerful legs and a strong body. Where they primarily differ, other than where and how the barbell is carried, is which muscles each exercise emphasises, how mobile you need to be to do them and where each one belongs in a training program. In general, you cannot front squat as much as you can back squat (about 85 per cent of your back squat). Since all of the weight sits in front of you, the actual squatting movement changes quite a bit, too. Rather than sit back and have a slight forward lean like you would in a back squat, you are squatting almost straight down. As a result, you emphasise your quads and upper back muscles a lot more in a front squat.
What's more, you need mobile wrists, lats, an upper back and healthy shoulders to be able to hold the weight in front of you. Some folks who lack the joint mobility get around this by using special wrist straps or crossing their arms like a mummy to balance the weight. But it's also necessary for you to have proper mobility in your hips, groin and ankles to front squat without your knees going over your toes or your back from rounding a whole bunch.
The back squat is generally considered better for building overall strength (because you can squat heavier), but the front squat is really useful for helping you build up the strength for another movement, like the clean, clean and jerk and snatch. You can actually include both in your program if you want. It simply means you can get more squatting done without hammering the exact same muscles.
Front Squat vs Back Squat [Brandon Campbell]