By parking it under the google brand they may have made a mistake. Another - possibly small - effect of that is that you have two steps before getting to a site, video.google.com, is less convenient than youtube.com, and much less easy to promote as a brand separate from the search portion of the site. Many people read 'video.google.com' the same way they promoted 'images.google.com', as a search engine for online videos (which it now has become, for the most part) instead of an easy way to share your videos with your buddies and the rest of the world.
I don't think it will be possible to quantify this effect, but I notice that microsoft named their search engine 'bing.com' after several tries of doing it as a subsidiary, and that google has not attempted to bring youtube.com under the google domain as the replacement for video.google.com (which still exists), it is now the 'search' arm of google for video, returning youtube.com mixed with other video results, just like what you'd expect.
Further thought: google video was 'better' in that it had higher resolution videos, and it displayed more of them on the screen at once. While youtube had one low resolution video. It was quicker to load and to run, and more suited to slower machines (perhaps especially mobile phones, whence videos oftentimes came?) Google video has always annoyed me in this sense. I note that now, they've increased youtube video resolution (it's 'better'), and also snipe: upgrade to a "modern" browser. Although understandable, it isn't the path to max adoption, and max. network effects