"..more links from non Irish sites"
That or a stricter relevancy filter in "web search" would be my guess.
As an example try "link schemes", page is at 4 in PFI and at 14 and first Irish result in "web search".
Problem there is that the relevancy filter in PFI seems banjaxed, so even if the higher ranked pages in the PFI results have a better ratio of Irish links it's hard to identify cause/effect.