Unfortunately, both. They have copyright and they can be scanned.
Originally Posted by ted_smith
If people are happy with the poor quality they can get by scanning and printing themselves, that's what they are going to do. I don't think you can do much about it other than to charge enough to cover the time you have spent working.
Especially with digital, I can see the business model for weddings changing so that the up front fee includes transfer of all rights to the customer as once they have files, you no longer have control.