ServerAlias not working

I have a VPS, that I have configured to host multiple websites with name based hosting. It is all good while only using example.com, and www.example.com. It also works with example.net, but when I try example.net, it reverts to my default site configuration, which just shows my default (empty) index.html page.

Here's the default file:

<VirtualHost *:80>
        ServerAdmin webmaster@localhost

        DocumentRoot /var/www
        <Directory />
                Options FollowSymLinks
                AllowOverride None
        </Directory>
        <Directory /var/www/>
                Options Indexes FollowSymLinks MultiViews
                AllowOverride All
                Order allow,deny
                allow from all
        </Directory>

        ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/
        <Directory "/usr/lib/cgi-bin">
                AllowOverride None
                Options +ExecCGI -MultiViews +SymLinksIfOwnerMatch
                Order allow,deny
                Allow from all
        </Directory>

        ErrorLog /var/log/apache2/error.log

        # Possible values include: debug, info, notice, warn, error, crit,
        # alert, emerg.
        LogLevel warn

        CustomLog /var/log/apache2/access.log combined

    Alias /doc/ "/usr/share/doc/"
    <Directory "/usr/share/doc/">
        Options Indexes MultiViews FollowSymLinks
        AllowOverride None
        Order deny,allow
        Deny from all
        Allow from 127.0.0.0/255.0.0.0 ::1/128
    </Directory>

</VirtualHost>

Here's a configuration for the example.com site:

    <VirtualHost *:80>
     ServerAdmin admin@example.com
     ServerName example.com
     ServerAlias www.example.com
     DocumentRoot /srv/www/example.com/public_html/
     ErrorLog /srv/www/example.com/logs/error.log
     CustomLog /srv/www/example.com/logs/access.log combined
<Directory /srv/www/example.com/public_html/>
AllowOverride All
Order allow,deny
allow from all
</Directory>
</VirtualHost>

And here is the config for the example.net site:

<VirtualHost *:80>
     ServerAdmin admin@example.net
     ServerName example.net
     ServerAlias www.example.net
     DocumentRoot /srv/www/example.net/public_html/
     ErrorLog /srv/www/example.net/logs/error.log
     CustomLog /srv/www/example.net/logs/access.log combined
<Directory /srv/www/example.net/public_html/>
AllowOverride All
Order allow,deny
allow from all
</Directory>
</VirtualHost>

Where could the problem be?

I believe, that there is something going wrong with the ServerAlias property.

Could it be because of the way the site's are built? Because example.com is a Joomla site, and example.net is a Zend Framework site. Just in case, I'll also insert the .htaccess files for example.net, since example.com has it's disabled:
example.net:

SetEnv APPLICATION_ENV development

RewriteRule  ^(browse|config).*  - [L]
ErrorDocument 500 /error-docs/500.shtml
SetEnv CACHE_OFFSET 2678400


<FilesMatch "\.(ico|pdf|flv|jpg|jpeg|png|gif|js|css|swf)$">
Header set Expires "Fri, 25 Sep 2037 19:30:32 GMT"
Header unset ETag
FileETag None
</FilesMatch>

RewriteEngine On
RewriteRule ^(adm|statistics) - [L]
RewriteRule ^/public/(.*)$ http://example.net/$1 [R]
RewriteRule ^(.*)$ public/$1 [L]

Any help would be greatly appreciated!

Edit So that my question is ABSOLUTELY clear:
The problem is, that one site works with both www prefix as well as without it, and the second one does not. I would like to know how to enable the second site to work with www prefix as well.