Some prescriptive grammarians would argue that the de- prefix should be used on verbs and un- should be used on adjectives.
So, you deregister something and it becomes unregistered, or you deselect something and it is now unselected.
The logic behind this is probably because de- only attaches to verbs to give the notion of reversal, so for the sake of order/non-redundancy/etc. you'd want un- to occupy the other domain: yielding the opposite meaning of an adjective it attaches to, and nothing else.
However, it has never really worked this way; the prefix redundancy among verbs is there, and it is very unlikely to disappear. Note that, most of the time, you can't just use whichever one you want — usually there is one preferred form. But whether it is un- or de- is something that varies on a word-by-word basis.
FumbleFingers mentioned something else in comments that is worth mentioning: un- seems to be much more widespread, even in the verbal realm, in the production of new words in the past few decades.