Answers:
Neither and both.
Unorganised means that whatever the item is it has not been organised in the first place.
Disorganised infers something that once was organised is no longer
Consider these:
The group of men were unarmed.
The group of men were disarmed
The first is a negative statement which shows a state AS IS
The second denotes a CHANGED-ALTERED STATE which can be more negative than the original one
Similarly:
John is unassociated with that company.
John is disassociated with that company
You can now see that in certain cases the prefixes un and dis can have quite a profound change in meaning let alone emphasis.
Un is really Non-something.Dis is really denoting an altered state and to a more negative one viz disjointed,dislocated,disencha...