[For example: If you have a car site and you had a choice of a link from a PR7 site that is all about “women’s dresses” which has nothing to do with your site or a relevant link from a PR1-PR3 site from a site all about “Cars”…. which link would help the most?]
I believe you are confused about the definition of “link relevance”. Anyone can come up with their own definition, but the only useful definition is is one that corresponds to Google’s definition of “link relevance”. Google’s definition of link relevance has absolutely nothing to do with the “site” topic. Google rankings are all about page-level signals, not “site” level signals.
So, if you have a link from a page that has no relevant content, then and only then do you have an irrelevant link. The mere act of adding relevant anchor text will make that link relevant, and it also makes that page relevant.
With a little creativity, you can make virtually any anchor text relevant to both the page topic as well as the landing page topic. In the example you gave above, placing a link to a page about cars on a page about lady’s dresses: i.e. Find the perfect car to go with that new dress!
While an irrelevant backlink will have no direct influence on your SERP ranking, you can get a smaller secondary influence if you channel the link juice through a relevant anchor downstream. You will never receive any ranking benefit until after you have channeled the link juice through a relevant anchor text.
I beg to differ, your OP suggests otherwise. Website topics have nothing to do with whether a link is relevant or not. This is a common misconception, so I attempted to clarify that in my reply.
Let’s assume that you do know what link relevancy is, you should also know that an irrelevant link has no direct influence on ranking. You receive absolutely no direct benefit from an irrelevant backlink, regardless of the PR. So your “irrelevant PR7” backlink has no direct ranking benefit.
Notice in the above assertions I used the adjective “direct”. That is because there is the possibility of an “indirect” benefit. Since this potential “indirect” benefit is conditioned upon certain subsequent circumstances, the correct answer is sometimes a PR1 relevant link is more valuable than an irrelevant PR7 link, and sometimes it isn’t.
Anyone who tells you either one is more valuable than the other will be wrong in some cases and correct in others. In my reply above I attempted to explain the conditions required for one option to be more valuable than the other. Please re-read my original reply and ask more questions if you do not understand.