While putting the search directly on the page eliminates one click for the user, a search field within a content page must be very basic. There still may be a need for a special search page if more complex queries are to be formed. It really isn't possible to put advanced search mechanisms within every page, as it tends to make the search facility too prominent and takes away from the page's primary purpose of delivering content. So the question is really to expose a simple search facility on content pages or provide it on a special search page. Regardless of the choice, search should be easily found from every page in a site.
Suggestion: When search is available in a site, include a search button or field on all pages.