A domain backlink links to your site’s domain (e.g. www.acme.com) and a page backlink links directly to a specific page within the domain, like a product or article page.  Martin Spiek Chief Search Officer of DEP Labs gives a great answer to “What is the value of domain vs page backlinks?”:

1. It really depends on the keywords or key phrases that are used by the consumers in their searches for products or services.  If the consumer searches are more detailed, specific and individually product relevant, then a single product or group of products can rank higher.
2. The higher ranking of specific products over “broad” subject matter also depends on the origin of the backlinks.  Does the origin web page of the backlinks consist of a “broad” or “narrow” subject matter and use similar keywords or key phrases in the origin page(s) as in the destination link / web pages?
3. The greater the continuity of keywords and key phrases (broad or narrow) of both the origin web page(s) and destination web page(s) will have the greatest linking benefit to the both the one way link association and most certainly in any reciprocal / traded link associations.
4. Consumer traffic, daily, weekly, monthly to the origin of the backlink is also critical in the quality of the link.  If the origin site has high consumer traffic on a regular basis this is a critical factor in the Quality Score of the backlink.  If the origin of the backlink has little or no regular consumer traffic then the back link is really of little or no value – no matter how good the subject relevancy or continuity from origin to destination is.
5. Does the origin site currently rank on Page 1 of Google, Yahoo or Bing for the keywords being used?  If the site is not in the top 3-5 pages of these popular search engines on the target keywords & key phrases then again the Quality of the link requires much greater review before creating the link association.
6. Popularity and subject continuity are very important components to relevancy as well as linking structures both internally and external inbound links.

Martin’s answer helps to clarify that not all backlinks are created equal and the typical SEO approach of getting lots and lots of backlinks to your site will not necessarily improve organic search traffic at all. Google and the other popular search engines are all about ensuring search results are relevant and this applies to backlinks as well.  Therefore, a well thought out backlink building campaign that targets sites of high quality will have a much higher impact on search ranking than getting thousands of poor quality backlinks.