I believe it is the relevancy of the page, related to the search term
Links for both inner pages and home page are equally important. But the question is if you are dealing with the purpose of business then you should go for that page whether it is inner or homepage.
They are all relevant however, some more relevant then others.
Example : One of my sites is a online chef recruitment site.
The front page has ranked for all keywords, but then there are intenal pages which are specific. So the page for head chef jobs is not going to be built for sous chefs.
That page has one specific keyword and is built for that keyword and of couse slight variations.
making sense ?
Both. Your home page is still the most spidered page on you site and is like the trunk of a tree. Deep pages are important, too to get serps for sections and keywords.