Minisite Better As Subdomain Or Another Domain?

I am helping someone build their companies SEO up. They currently have a busy site but they are always trying to beat out the competitors. I suggested a minisite around one of their topics.

Overall, would the SEO of their brand (they make stuff under a brand) be better off if the minisite was part of their main site (i.e. brandname dot com forward widgets) or as a separate site (i.e. widgets dot com... which links to the main brandname dot com site)?

Thanks!