They're both buggy as hell, the type of bugs that will make your document render in unintended ways when somebody opens it on the other side. At some point, Word for Mac decided to remove whitespace between words on my resume - I couldn't see them and generally exported to PDF, but I didn't hear back from prospective jobs that asked for a word format specifically.
Office 365 Web and desktop application really need a complete revamp, they have reproducible bugs and horrible UI/UX in edge cases.
I also really hate when Microsoft decides I want to store my sensitive data on their cloud for no apparent reason despite saving to local disk, it really seems like a 'whoops we accidentally did this but you should try it!' kind of move from MS. This is the perfect example of a monolithic application with chronic feature creep.