I came to this article as suggested by "Microsoft® Exchange Server Profile Analyzer." There, a section called "Configuring Accounts on Exchange Server 2007" mentions
To add full mailbox permissions on all mailboxes stored on an Exchange server or on an
individual mailbox store, locate the Microsoft Exchange Server 2007 Help, and search for
the topic, "Add-ADPermission."
It does not mention accessrights fullaccess, which seems much appropriate. Why not say
add-mailboxpermission -identity Mailbox -user MailboxFullAccess -accessrightsfullaccess
see this link for more
http://www.experts-exchange.com/Software/Server_Software/Email_Servers/Exchange/Q_22867913.html