Hi geekgirl. Since this is more an SEO issue than a domain issue I moved this over to the preferred location for SEO issues.
I'm not the expert but I'm going to kick this off by suggesting that "the" (an) answer - especially since your company appears open to a sub-domain solution - might be "neither" . . unless the solution is impossible to add-on via a sub-directory of the existing site. In other words go with adding the functionality via adding a directory versus a sub-domain.
From a link juice perspective the guidance I last understood was that search engines, to avoid "gaming by sub-domain", were treating subdomains essentially as "new" domains. That approach somewhat makes sense, especially where the "new (sub) domain" isn't quite within the theme/authority/trust of the original site.