First of all, office software suites have matured significantly over the last year. It wasn't that long ago that Google Apps wasn't really ready for prime time. But as the cloud has matured, and as people started using cloud-based applications, maturity came quickly. Sometime last year, Microsoft began work in earnest to create a version of Office that would compete with, and hopefully beat, Google.
After all of the testing and the analysis, it's clear that Google Apps has become a very good product. It's also clear that Office 365 is a very good product, and it has some features that you won't find with Google. But the gap is probably more narrow than you might expect. Office 365 is very much like using Microsoft Office. In fact, for most companies, it actually is Microsoft Office. Google Apps for Business, meanwhile, has now added the ability to interface with Microsoft Office much more than it has in the past.
There are some important differences that may affect your company, however. First, Google requires that you transition to Gmail. To use Google Apps for Business, you must insert a piece of mail redirection code into your DNS entry. In addition, you must insert code into your website's meta data or its DNS entry to prove that the website you're giving Google is really your site.
Microsoft Office 365 provides a cloud-based Exchange Server, and a cloud-based version of Outlook, but you're not required to use them. If you already have a hosted mail server and want to stay with that, you can. You can also run both mail systems in parallel if you wish. This makes transition vastly easier than with Google because you can make the transition at your own pace, if you transition at all.
Microsoft Office 365 offers cloud-based versions of its applications; they work well, but don't have all of the features you'll find in Microsoft Office on your computer. Google Apps for Business has similar features, but it's entirely cloud-based. There is no version for running the software on your PC. This means that you're tied to the Internet if you want to work, and there are times when you can't use the Internet - like on an airplane flight, for example.
Of course, you can still create documents using Microsoft Office on your PC and then transfer them to Google Apps, but I found in my testing that not all documents created this way transfer successfully. Occasionally they're garbled to the point of being unusable.
So which should you choose? Google Apps for Business is slightly cheaper, and it's very widespread. More important, a lot of people are familiar with it. Microsoft Office, on the other hand, has effectively no learning curve since virtually everyone in business already uses it. The pain of entry for Google Apps for Business is higher than it is for Microsoft Office 365, but Office 365 costs slightly more per seat. The answer, of course, is to try both. There is a free trial of Office 365 at http://www.office365.com and a free trial of Google Apps for Business at http://www.google.com/apps. You can see for yourself which one fits your business the best.