I was catching up on the returned www.jkontherun.com (excited for James's return to this venue), and I came across his post about Apple's Continuity features in OSX and iOS.
I started a comment but it got a little long, so read his post, and come back over, I'll wait.
Microsoft does have several of these features, in some form. Windows 8, 8.1, and 10 when paired with Windows Mobile 8, 8.1, and 10, share the same WiFi hotspot capability.
Windows 8 and 8.1 enabled profile syncing (start screen, colors, and apps) across devices - this was unfortunately deprecated in Win10 for reasons unknown, I'm hoping it returns. There were also (more limited) syncing capabilities across Windows and Windows Phone.
The Windows app platform enables apps to sync settings across devices, so you only have to configure once and they "just work" on other devices.
Where these and Apple's continuum fall short is cross platform - fact is most people have Windows PCs, and Android, and then iOS devices.
Over the last couple of years Microsoft has done a great job here - for years OneNote has been cross platform, and it has gotten better with deep OneDrive integration over the past couple of iterations. I can now pick up literally any device I own and access any of my notes.
Same goes for any file on OneDrive - and with unlimited storage as part of Office365, that's where all of my files live. Including photos - which are automatically backed up from my various Windows, iOS, and Android devices.
In the last year (with the long awaited release on Windows) Microsoft has also brought this convenience to Office. Your recent files lists are synced in the current Office apps across devices. So I can at ease puck up whichever device, and not have to remember whew that file was stored (OneDrive, SharePoint, etc.)
Microsoft has done a great job of integrating within their ecosystem, and more importantly (I suspect largely die to their weak position in Windows Mobile) across platforms as well.