How is this a Firefox browser issue?

Because I am using Firefox when the stuttering occurs - so its possible one of the millions of users who use both FF and VLC have experienced something similar and may be able to provide a solution

If your playing video and downloading video the CPU is most likely overtaxed and that has a system performance downside as result of the playback. Do you have a standalone GPU or integrated GPU/CPU processor? It's never to play and download video as that taxes your CPU/GPU and RAM to run a heavy task like that. So unless you have 16Gig RAM and Dedicate GPU playing video on the same machine your downloading will tax the system resources to play and download a large video at the same time. You should first try VLC to play without browser downloading and see what happens if that has no issue then it would mean your system isn't configured to optimize video download and playback as they use system resource to do the same process. Also restart your system every so often to insure it's peak performance.