So, is this on one computer or two?
Are they both using the same monitor?
For two monitors to display the same data the same way, they need to be colour managed. For different applications to display the same data the same way, they need to be colour managed.
In a colour managed browser a correctly tagged image will be displayed correctly. You need to ensure the image is correctly tagged, and that the browser is colour managed. Then the monitor needs to be profiled to display the data the same way as another profiled monitor.
I’m afraid you have entered a world of pain, but it is very rewarding once you are aware of how to handle the issues that may come up.
The V2 profile may be a little old now. Perhaps try again with the V4. This site has some test images you can use and will walk you through checking colour management is on for Firefox:- http://www.gballard.net/firefox/#config
I don’t have Chrome to test with, but I would trust Firefox to get it right more than Chrome. Some simple image viewing applications may not be colour managed at all. Windows is a different environment again with the same issues.
EDIT - I didn’t read all of this (it’s late here), but maybe it’s relevant:- http://cameratico.com/guides/google-chrome-color-management/