The advantage of securing documents with certificates is that authors can specify unique permissions for each person. For example, authors can permit a person to fill in forms and comment in document, and permit another person to edit text or delete pages. You can choose certificates from files on disk, or from the Windows certificate store. Only a specific set of users whose identities can be verified and managed can have access to the document. A certificate that contains public key and other identifying information is used to encrypt documents, or verified a digital signature. Only corresponding private key decrypts the document that was encrypting using the certificate.
Generally, if possible, encrypt documents using certificates from third-party provider. If the certificate is lost or stolen, the issuing authority can replace it, if a self-signed certificate is deleted, all PDFs encrypted using the certificate is forever inaccessible.