A shared mailbox is a good solution when you need a single repository for mail coming in to a particular address:
With a distribution list, copies of an email sent to the list are sent out to each of the members of the list, and those copies operate independently. If one person should hit Reply without Reply all, other members of the distribution list won't be CC'd or have any way to know that one member responded.
A shared mailbox functions in many regards just like your user mailbox; mail comes to it and stays there, in its own mailbox. Someone with rights to the shared mailbox can reply to a message that's ...