I've heard that for SEO and usability in general it's better to have them at example.com/forums.
I disagree. It shouldn't make a signficant difference.
Regarding security and maintainability, however, it would be better to host the forums in a seperate VirtualHost (or to be exact, a seperate cPanel account).
Yes; and quite apart from server-side security issues, there's also the client side. If you put your forums on the same hostname as the rest of your site, any cross-site-scripting vulnerabilities in the forum software (and there are almost always cross-site-scripting vulnerabilities in forum software) immediately become cross-site-scripting vulnernabilities for your main site. If you've got anything sensitive on that site like accounts or admin pages, your forum has compromised your mission-critical stuff.
So keep your forums on
forums.example.com and your main site on
www.example.com, where they won't be able to leak each others' cookies.