I wouldn't use either by themselves. What are your forums about? What phrase will people use to search for your forums? This can give you a one-up on search if you make that phrase what people type. Are your forums about cars? Go for domain.com/carforums or domain.com/carforum.
To add some more spice. What would be better forums.website.com or website.com/forums If you use the 2nd option are you likely to get more traffic if this domain is alot more established than the first subdomain ? Are there any advantages of using either when it comes to forums?
How big will your web site be? If you ever need to put your forum on its own server, it's much easier to split off forums.website.com rather than website.com/forums. Usually it's not too big a deal, though, to just move the database to a different server or servers. There can be some slight SEO benefits to having it as a separate domain in forums.website.com. Depending on the search engine's algorhythm, it may give you more rank by having the forum point to your www than it would as an internal page linking a menu. In either case, it is not a major thing. I think a lot of Internet users are more comfortable with website.com/forums. So, my opinion is technically forums.website.com has an advantage, but the human usability factor of website.com/forums outweighs any technical advantage. Of course, if your forums are for tech type people, the human factor can diminish to a large degree.
May I suggest: forum.yoursite.com instead of yoursite.com/forum And forum is better, but redirect forums to forum.
It confuses me cause some use one, others use the other. Do both, just redirect the secondary one to the primary one.