I know how a box squat is done and how a squat is done. But I don’t know why using a box to stop the downward motion is of any help. So basically my question is, what is the purpose of box squats? I’ve read on them a little but I want to hear what people who have tried them have to say about them, when should one use box squats instead of squats and vice versa?
Edit: westside style box squats
The very best thing about box squats is that you know that you hit the same depth on every squat. It makes progress easier to follow, etc. It also stops the ‘bouncing’ motion some people might have, and make you contract muscles more than if you are just bouncing up and down like a Crossfit maniac.
To clarify, by ‘box squats’ are you refering to westside style box squats or just a standard squat to a box or bench?
The box also helps break the tension in the legs, killing any elasticity. This really helps develop explosive upward drive with the Pchain. So ong as you keep a solid hip tilt and a rigid back including box squats will really help train your power out of the “hole” as it were.
-chris
Do you mean a bb’ing squat where the squat is done the same precise way, except that the box is lightly touched before reversing?
In this case that sort of “box squat” (but most do not mean this by this term) indeed does nothing except mark depth.
The powerlifting box squat is not like this.
Instead, one sits back moreso than if a box were not used, and tension is taken off the muscles by putting weight on the box. This eliminates stored energy, which makes the lift harder.
Additionally, sitting back further seems to emphasize the posterior chain more.
Box squats allow you to learn a better path in the move, to sit back more instead of leaning forward.
This is VERY difficult to learn without a box to ‘sit back on’.
It also allows you (as mentioned) to pause on the box momentarily and squat from a dead stop - which will increase strength at that portion of the lift - which is handy as it is the hardest! 
Just as power/sumo squats and front squats are vastly different from the ‘regular’ back squat - box squats are also a very useful variant.
I assume you have never done them? Do them and you will see all that for yourself.
PLUS - before my post shows…
It is NEVER a matter of either or… you rotate all exercises in your routine, for all muscle groups.
Do both.
On a side note - are those legs yours? You will be able to build those into some very large and muscular thighs mate - lucky you.
thanks for all the responses guys, just for clarification, I meant powerlifting style box squats. I have done squats to a bench to mark depth but never box squats and the reason I want to know how they compare against normal squats is because I was reading some Defranco articles about vertical jumping, which spiked my curiosity, why box squats?
I perosnally don’t think you need them.
I got my squat big by just doing regular squats heavy n hard, and often.
I do squats with oly shoes with a narrow stance, and I do squats with flat shoes, a bit wider stance (not so much to kill the hips as you see westside style) and if you’ve been squatingg for any amount of time you’ll know if your hitting depth or not.
I also like to include pause squats here n there…Squat, stay in the hole for 3 seconds. Drive out.
I like that much better.
For anyone that’s interested, here’s a link to a video that explains the advantages of box squats for power athletes.
www.powerliftingwatch.com/node/6608
In addition to the above comments, when squatting in a squat suit, the suit will bind up in the hole. It will more or less lock up and not allow you to go any further downwards. ‘All’ you have to do at this point is push the weight back up.
If you lift raw, box squats probably won’t help your squat much.In fact they might hamper your squat by you ‘unlearning’ to use the stretch reflex- it did that for me anyways. I had gotten so used to relying on the box to more or less stop the weight. When I free squatted I got stapled with a weight I could easily rep out with on the box. Wide box squats will help you if you pull SUMO.