"Assuming that all things are equal..."
All things are equal. I am not assuming. Each browser window is really getting exactly the same page and exactly the same resources.
(Well, in the few seconds it took between "document ready" in browser window #1 and "document ready" in window #2, Earth had moved a few hundred miles across the universe. Thus, the entire nature of reality could have shifted ever so slightly. But I doubt that would be the cause.)
Can we then say that a browser could:
Then I would say we have found the culprit -- a difference in the operation of the browser depending on the page's host. Such a difference in operation would be by the browser - not the server.