iOS is based on OS X though, but anyway the technical distinction is irrelevant to my point.
The point is that Apple integration is very tight across devices, in a way that must be very appealing to Microsoft from a business perspective.
But Microsoft has it's own strengths, such as catering to the support and feature needs of the enterprise. In a way it mirrors Apple's strategy of targeting the high-end consumer market, Microsoft targets the highest-end software market, period.
The difference between "based-on" and "Windows everywhere" is subtle, but makes for a huge difference. Apple is willing to fit the right parts in place where Microsoft has made some truly bad and confusing technology selections (e.g. full Windows on tablets instead of a grown-up phone OS).
The difference is the quality of execution. I don't think "Windows everywhere" implies the crap they've been putting out. I chalk it up more to incompetent middle management.
The point is that Apple integration is very tight across devices, in a way that must be very appealing to Microsoft from a business perspective.
But Microsoft has it's own strengths, such as catering to the support and feature needs of the enterprise. In a way it mirrors Apple's strategy of targeting the high-end consumer market, Microsoft targets the highest-end software market, period.