Not 'identical, expect for the normal wide to small color space changes you would expect'.
virtually all monitors except laptops, which are often narrower than sRGB). What should happen in a colour-managed viewer: these two images should look identical on any calibrated/profiled monitor that has sRGB gamut or larger (i.e.
Some browsers don't colour manage properly, and AFAIK all browsers use only the main monitor profile, so you can't usefully compare images on multiple monitors in a browser. Note: I've included these as images to download, as viewing images in browsers is misleading. The first version is an sRGB version (so no colours outside sRGB gamut), the second is the same image, but converted from sRGB to Adobe RGB (so it still won't have any colours outside sRGB gamut). To demonstrate that the Photos app ignores both image and monitor profile, you need two calibrated and profiled monitors, one wide-gamut and one standard-gamut (but the latter at least as wide as sRGB).
Here's how to test, and what I think the test shows. It doesn't use either the monitor profile or the image profile. I don't think the W10 Photos app is colour managed, not even part colour managed.
