Wondering why in the search engines index, your Joomla! links appear both with and without "www" ?
Until you set the preferred domain to tell search engines how to display URLs in their index, the website will have issues with duplicate content.
SEO disadvantages:
The pagerank will be divided to both versions of the website.
Not to mention that spiders will have a harder time to discover the fresh content because they will be forced to index both versions of your Joomla! website. (spiders have limited bandwidth when crawling a website).
This duplicate content issue can be eliminated easily:
1. choose from Google Webmasters Tools the preferred domain
2. set a 301 redirect