Always remember that search engines do not consider "websites" they consider the "pages" of those websites. There should never be a debate as to which is more important between "on page" and "off page" characteristics as the truth is both are equally as important.

On Page Characteristics are anything you can effect within the construction of a single page. This includes everything that is placed in the headers, body, and on-page links (both internal and external). Special attention should be given to: Title, meta description, H1, H2…H6, <b>, <i>. Keyword proximity, keyword density and relevance..

Off Page Characteristics refer to all links (both from pages contained within your own website and from pages of other websites) that point to your specific page(s). The term "pagerank" is specifically designated to evaluate and weight "off page" criteria. Special attention should be given to: anchor text, Reference_tags, "title" attribute and "target_" etc