If it's a new install of the OS then things like downloads will seem faster at first. It's always the case that the OS boots in seconds and you're amazed at the power of the new PC. Then you install the proper graphics drivers, the proper audio drivers, put on an AV, and before you know it it's creaking along as before. All the nice new drivers would have come with their "management uilities" which will all be phoning home regularly to check for updates (or in the case of something like Avast AV, it just openly admits it's recording everything you do and uploading it to their servers).
It's also possible that old OS had some genuine malware or adware that was draining your bandwidth.
The odds of your internal network being slower than your internet connection are incredibly slim.