The best SEO example in the hosting world is DigitalOcean. Look at their marketing/sales (main site) and content (tutorials/community questions) - note which domain those are on. That’s all I’m saying. Billing/service control panel can be on another subdomain.
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Subdomain.
It will be easier to manage.
Having a subdomain will enable you put/host the applications (in your case, the knowledgebase) on a completely different server. So security-wise it will be a better option.
But as @Harambe mentioned, you could still achieve that with a subdirectory via a reverse proxy. Obviously you could argue that while the subdirectory could indeed be hosted elsewhere, the proxy itself will still remain on the root site’s server. So from that perspective, you’re correct.
Overall, I’ll probably host secure/important things via a subdomain and then use subdirectories for things that don’t really need that added layer of security on top of the security practices already in place.