Oh it makes a big difference.
But how to answer the question can kinda depend on your school of thought. I.E. if we are going to compare the olympic back squat to the
power squat (low bar, wide stance, etc) then you can talk about more in depth differences.
But if you are just going to compare the mechanics of them then the post I made a couple of posts before sums that up. So the low bar position will put more of it on the PC, will not be as deep, etc..
I think people are not starting with the basic fundamentals when they talk about this stuff. So people talk about low bar squats and they say things like "with low bar squats you need to focus on bringing the hips back more or
sit back, in other words) whereas with high bar squats you shouldn't do this. But this is really getting ahead of the game.
You take light enough weights, and take basic squat tenants while you learn the movements, the body must put the weight in the proper position, that position changing depending on the person and the bar position, and the stance width. You will be limited by all that or freed by it depending on your circumstances.
Actually, I was just discussing this in a pm. If you do a front plate squat, then a goblet squat, then a front squat, than a high bar "olympic" back squat, then a low bar squat you will see first hand the changes that makes. Including how deep you can go, etc. Keep in mind that a wider stance is usually taken with a lower bar position. Try it with a narrower stance and you'll probably see why. (People also think a wider stance makes for more hamstring contribution but this is kinematic nonnsense, it just recruits the adductors a bit more).
Mike Robertson and Geoff Neuport have a good article comparing olympic squats to power squats..
http://www.t-nation.com/readArticle.do?id=1736931