It's a different format--merely copying over won't work.
I think Jamie has built an mbox to Maildir converter into one of the migration tools for cPanel or Plesk or Ensim...yep, there's a little snippet of code in the cPanel migration script to convert using the various mail libraries in Webmin. I'll see about getting this turned into a standalone script in the future...maybe in the form of a complete "Switch me over to Maildir" script that'll make sure all of the other bits are set correctly in Postfix, Dovecot, and Procmail (if being used).
In the meantime, there are some good scripts out on the web to make the change--conversion isn't terribly complex, as they are both plain text formats with just a few bits of special data.
I believe this is the one I've always used:
http://untroubled.org/mbox2maildirThough this one looks a lot nicer (but requires the TimeDate Perl module--though this is available in the repos of most modern Linux distros, I think, and if not you can use the Webmin CPAN modules module to install it):
http://batleth.sapienti-sat.org/projects/mb2md/I think I'd probably go with mb2md if I were in your shoes today.