Either way is fine, but if you ever change domain names, then you'll have to change all of those links. Relative links are better, especially relative to the document root (links starting with /). Speed wouldn't be a noticeable factor.
It doesn't really matter, when you think of the way your browser works.
When your browser follows a relative link, it works out the absolute link based on the directory the current page is in.
So the request to the server is the same either way.
However, make sure you are consistent with your links. If you have a page called http://www.myhost.com/thispage/ , then don't refer to it later as "thispage" (without the trailing slash) or "thispage/index.htm". Even though they may find the same page, the request to the server is different and thus caching is not working.
You could, however, refer to it just as "/thispage/" or "../../../thispage/" etc, as the browser will translate that to "http://www.myhost.com/thispage/"