Microsites offer content highly segmented to a specific audience. It is kind of a branded content site, differentiated from the main website of the brand. It has a different domain (or subdomain), different navigation, etc than the main one. Therefore, microsites are really useful as a marketing tool for raising brand awareness (in general terms).
Landing pages have more specific goals. They are pages inside the main site of the brand, to which the consumer is directed for a specific CTA. While a microsite can have more than one page (usually around 3), a landing page is only one. It’s useful for directing the attention towards one specific product/ service/ action.