Although both are spaniels, and there are obviously a lot of similarities, they do have some quite large differences.
From my experience (and this is only personal experience, not law), i'd say that cockers take a bit longer to mature, and can be a little more challenging to train in some aspects.
They hunt in a different manner, a little less formulaic, they seem a bit loathe to enter cover which they don't think holds, whereas the springers we have will work whatever you direct them to, regardless of whether its holding game.
I find the cockers a little like children, they can get a bit over excited, and get carried away, taking a bit more to keep on top of, but in general are sweet wee things.
At the end of the day it's horses for courses though, and one breed will suit one man / woman better than the other, and suit some situations better.
Having said that, a well bred and trained cocker will beat a poorly bred springer every time, and vice versa.
I personally like a good springer for beating, a good lab for picking up and a good cocker for shooting over.