Having both www and non-www versions of your website is a luxury. Search engines mostly treat them as two separate pages. If you have all the backlinks pointing to one of these only, all is fine, that is rare and hard to control occurrence, though. If you are running on an Apache server, just choose the one you like better and redirect the other via mod_rewrite.
The previous owner of a domain I acquired recently was using the short version, but was somewhat inconsistent in that effort, so both URLs had many backlinks and Google Pagerank which is hidden now.
Here is an example of a code that I used to redirect the non-prefix version to that starting with www:
RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} !^www\.example\.com$ [NC]
RewriteRule ^.*$ http://www.example.com%{REQUEST_URI} [R=301,L]
Slight variations to these 2-4 lines exist, if you are unsure, look them up on the net. While it is too early to report how the change affected my website, I am sure it is good if only for consistency reasons. The permanent rewrite is reported to pass Google link juice, so I hope to see at least a minimal increase at the next update.