PC vs Apple color management

To say another way what davescm correctly said, sRGB and P3 are just system defaults – for when a document doesn’t already have its own color profile. So the first part of this is that if a document already does have its own color profile, that is the color space in which Photoshop will edit it, Windows or Mac. The second part of this is about the accuracy of the display profile; to get good results on Windows or Mac the display profile needs to be customized to accurately represent the display actually in use, not just a generic profile.

For example, this works the same way on Windows or Mac: If you receive a document with an embedded Adobe RGB color profile, and the display profile is accurate, it should look consistent on Windows or Mac (within the limitations of the exact displays being used; that is why we say the color is “consistent” and not “exact”). The same is true if it is an sRGB or P3 document. Because as davescm said, if someone has color management set up properly, the color management system will reconcile the differences between the document profile and the display profile so that the color looks as consistent as possible across systems.

Yes, it’s true that P3 is larger than sRGB. But Adobe RGB is similarly larger than sRGB and both Windows and Mac users have worked with that productively for years on non-Adobe RGB displays...if color management, document profiles, and display profiles are set up properly.

Finally, ever since Microsoft rolled out their Surface Studio desktop with a DCI-P3 display, the differences between Windows and Mac have gotten even smaller. Because it is now possible to encounter — on Windows, Mac, and also mobile — a display that might be based on sRGB, P3, or Adobe RGB. There are no more platform-specific gamut standards. Again, properly configured color management helps ensure color consistency across all of those display gamuts, Windows or Mac.

In short: color management is determined by the application, not the operating system. There is no operating system color management. But there are color managed applications.

There are some technical differences in how it's implemented, but functionally, from the user's viewpoint, it's exactly the same.

Windows doesn't 'use' sRGB. 

A display may have an sRGB color gamut (that alone doesn't make it sRGB), it may not. 

An application may be color managed or it may not be. 

Non color managed applications have no idea what sRGB is; that requires color management. Ditto with DCI-P3 or any other color space. 

You can't control how others view your images; do they have color management products, are they calibrating their displays and if so, how? They can differ. 

See: 

sRGB urban legend & myths Part 2

In this 17 minute video, I'll discuss some more sRGB misinformation and cover:
When to use sRGB and what to expect on the web and mobile devices
How sRGB doesn't insure a visual match without color management, how to check
The downsides of an all sRGB workflow sRGB's color gamut vs. "professional" output devices
The future of sRGB and wide gamut display technology
Photo print labs that demand sRGB for output
High resolution: http://digitaldog.net/files/sRGBMythsPart2.mp4
Low resolution on YouTube: https://www.youtube.com/watch?v=WyvVUL1gWVs

Colour managed applications (such as Photoshop, Illustrator, InDesign) will use the colour profile of the document and convert it, in the background, using the output profile (display or screen) for the most accurate output within the gamut of that output device. That applies whether the document is sRGB, AdobeRGB, DCI-P3, ProPhoto or any other, provided the applications are set to use the embedded profiles. In Photoshop that means setting colour settings to  "Preserve Embedded Profiles" and ensuring that the ouput profile is accurate (so that means using a monitor profile made for your monitor and a printer profile for your particular printer/ink/media combination).

Colour managed browsers will do the same. 

However, non-colour managed applications will display incorrectly. Just how incorrect they will be depends on the colour space of the document and the gamut of the output device. Some of those applications could be 'sort of' close using sRGB documents and narrow gamut (close to sRGB) monitors. That is why you sometimes see the advice to use sRGB when sending documents into the big wide world. However that does not give accurate colour  and falls down on wide gamut monitors for which proper colour management is essential.

In short - with proper colour management enabled - it does not matter.

Dave