Microsoft has their own on-line, cloud based education document sharing portal, based on their Office 365 service. While also free to educators, it is not as widely deployed as Google Docs.
However, things change quickly on the Internet and Office 365 is definitely worth considering, especially if you ware already comfortable with Microsoft applications.
Microsoft's introductory page on their free Office for Education offering. Requires a school email address to get started.
Scroll down past the Get Started form to learn more about Office 365.
Office 365 Education, their Internet based solution, is free for your entire school. For a small fee per student, you can add installed copies of Office on PC and mobile platforms, analytics tools and additional features.
This June, 2013 Infoweek article takes a look at two different school systems, and what factors went into choosing the products they did.
This September 2015 article looks at 8 key differences between Google Apps for Education (now called G Suite) and Office 365. The article is written more for tech geeks than the average educator, but brings up issues worth considering.
An in depth article from ComputerWOrld UK compares the two offerings. Their take is that G Suite takes a minimalist approach, which makes it best for ease-of-use and getting everyone up-to-speed quickly, while Office 365 is feature rich and capable of processing complex documents and large amounts of data – which may not be a problem for most schools.