Well, it is a message board, so useful information tends to be current topics of discussion, which are newly created threads. When there's a current topic that happened to be discussed in a very old thread, I'd say 90% of the time people are just creating a new thread anyway.
Is migrating only the structure and usernames cheaper/easier? If that's the case, I think it's a no-brainer- especially if there's an archive.
Also, think of the usability of the boards with fresh content. Less volume of content makes searching for older threads easier, and may encourage users to do that more often, rather than create duplicates. By the time the board fills back up, perhaps users will have adopted better habits.
Typically with things like data migrations, the effort involved is the planning of the migration, not so much the volume of data being moved. That's usually easy to scale. So I imagine, from an effort standpoint, if he keeps any old posts, it's just as much of a hassle as keeping all of them.