For Google Drive and Google Keep, a major pro is that they are free and easy to share and organize. Google Drive specifically makes it incredibly easy to collaborate and stay very organized. As a writer, I personally am using Drive to type this write now. Google Keep is a note app that allows you to share notes with anyone and updates in real time.
For MS Word, the major pro is that it is still an industry standard, everyone knows how to use it, and it has a ton of features. You can do customizable toolbars, great formatting options, already-known keyboard shortcuts, and you can share and collaborate, as well as track changes. Of course the automatica catching of spelling and grammar errors are a huge help, too.
Google Drive and Keep are both tied directly to your email address and anyone can share anything with you if they know your email. If you aren’t careful about naming things in a way that makes sense, Google Drive can get overwhelming and messy. Also, Google Drive can lag a bit if the document is 50,000 words and over.
MS Word is not free. You’ll spend $80+ for the license for one computer. Plus, it can be pretty distracting and has a ton of features you probably won’t use. Another con is when moving documents from older versions of Word, you often lose formatting, and the newest versions can be somewhat confusing to find certain features. Older versions felt more intuitive.