This situation is similar to the choice that users had back in the mid-1990s between Microsoft Windows and IBM OS/2. Although OS/2 was a better operating system from a technical perspective, Windows did a much better job of running and integrating the DOS applications that most users had at the time. Everyone wants new and better software, but they don't want to lose the ability to use what they've had for years. That's especially true for businesses.
Both Google and Microsoft want to "own" your domain by providing core features like email and calendars. The winner in that battle will likely be the company that has the best balance between new features and support for existing documents. With so many users already invested in Microsoft Office, it would seem that Microsoft has the upper hand as business transition to the cloud. That's why Google Cloud Connect is so critical, because it gives Office-centric businesses the cover to move to Google Docs.
Legacy applications and documents are the torture that any new technology has to endure in order to be successful. Both Office 365 and Cloud Connect recognize that fact, but accommodate it in different ways. At the moment, both are unfinished so it's not clear which approach will be more successful. For most businesses, the company that can handle existing Office documents but provide a path to a better way to work in the cloud will have the upper hand.