Hey Josh,
Goog does differentiate the two in terms of applying link juice, but unless for some reason they deliver different content, it's not a major problem. My website has had this issue for awhile due to issues with our CMS system. There is an easy fix though. Try incorporating the rel canonical tag into your pages. Lots of great write-ups on SEOMoz and elsewhere on the usefulness of this tag - essentially tells Google which version of the url to credit the link juice and to keep in its index.
Then, as you said, I would change the internal link structure to reflect the "www" or "non-www" dependent on which one has the most links (Keep the one most people have linked to determined by a OpenSiteExplorer report from SEOMoz) so as to maintain consistency from that point forward. Ideally, you'd be able to 301 the less-linked version to the other since you lose a fraction of link juice with a 301.
Done correctly, you may actually gain engine authority since both non-www and www versions would "funnel" all of their link juice together.
Good luck!