As I used to work as a user researcher on Office:Mac, I can tell you that there has been plenty of research on this very topic.  However, I can't share specific results, since that research is proprietary to Microsoft.  With that in mind, I can share some things about conducting this sort of research in general.  

The first is that the environment of the organization matters a great deal.  Off the top of my head, here are some examples of barriers to change in the organization's environment: 

* the organization relies on a lot of applications that aren't available on the new platform
* the organization uses a lot of websites that won't work in the browsers available for the new platform
* IT for the organization isn't educated on and prepared to support the new platform

If there are barriers like this exist in the organization, then converting to the new platform will be somewhere between difficult and impossible.  If the environment is more open and amenable to supporting multiple platforms, which we're seeing more and more with the rise of BYOD (Bring Your Own Device) and now BYOL (Bring Your Own Laptop), such a conversion has lower barriers.

The second is that this isn't so much a question of usability (which is about being able to complete tasks the first time you encounter the new product), but rather of usage (which includes usability, learnability, and other factors).  No matter how well-designed a product is, if someone is used to using something else, switching to a new product is going to incur a cost because the user has a lot of expectations and habits that were formed using the previous product.  These expectations and habits are likely to be broken, and cause initial pain as a result, in making this switch.  The true test of the success of such a switch is measured a few months after the switch occurs.  Back when I was working for Microsoft, I wrote a [blog post about usability versus usage, considering the then-new iPhone][1], which has more details about the difference between them.

Overall, I don't think that it's possible to make a general statement about whether an operating system is better than another at the level of an organization.  Different organizations have different needs, different tools, different goals, and different users with different behaviors, habits, and expectations.  It's a varied world out there, and there's lots of great and valid reasons for that variability.


  [1]: https://docs.microsoft.com/en-us/archive/blogs/nadyne/usability-versus-usage-an-iphone-example