Not necessarily. The server is as secure as you make it. The security of a dedicated server and a VPS are almost identical in the sense that you will have to configure and optimize your server software and install any helpful additions (ClamAV, MailScanner, CSF, iptables, php.ini hardening, httpd.conf optimization, etc.)
If your provider manages the dedicated server they will most likely have their hardware firewall and certain protection which you might have to buy as an addon to your dedicated server. Other than that, it's practically the same.