The ranking would depend on the overall content quality of the page. The text that is selected to be added on the page, describing the video should be original and relevant to the context you wish to optimize the page for.
I believe adding the video on YouTube or saving it on the website won't make any difference. We have a website as a collection of YouTube videos ranking on top spot for a significant number of keywords we are working on. Yes, having the word video in the URL and title can help as a plus in ranking factors.