Performance Is the Biggest Differentiator
Once you're past the implementation part of using either of these cloud-based suites, there are still differences, but to some extent, whether they're better or worse depends on your needs. The Google management interface is rather terse, but once you're experienced in using the interface, that may be a good thing. The Microsoft Office 365 management interface is more verbose and more complex than Google's, but it also has greater functionality. Effectively, Office 365 managers have more granular control than do Google Apps managers. Both suites now feature cloud-based collaboration features. Google has just added Google Cloud Connect as a multiuser collaboration feature designed for Microsoft Office software. Microsoft offers a cloud version of SharePoint. Both allow multiple people to work on the same document at the same time. Google makes a point about not needing SharePoint deployment on its pages. But with Office 365, SharePoint is already deployed. All you need to do is use it.
Where users will see the biggest difference is in some areas of performance. While you can use Microsoft Outlook with either Gmail or with Office 365's version of Exchange, there are other areas where being able to use a locally-based application such as Word or Excel may be preferable. Because most businesses of any size already have Microsoft Office on their computers, employees can create documents locally and save them to SharePoint. Using Google Apps means you're using Google Docs, and depending on your Internet connection, you can have some latency-induced performance issues. I've noticed substantial delays in working with Google Docs documents online.