Which ranking is more meaningful for post-doc students? There were several discussions on this website about the importance of academic rankings. Opinions seem to range from "very important" to "completely meaningless". My question, however, is a bit different: Out of the different available rankings, which one is the best to consult when considering post-doc opportunities?

Of course, ranking is not an exact science. If one ranking claims university X is 23rd in the world, and the second ranking claims it's 27th in the world, there is little point in debating which one is "more reliable". However, the differences between the different rankings are sometimes huge.

Since I am a mathematician, let us consider for example the QS ranking and the Shanghai ranking in mathematics. The "glitch" of King Abdulaziz University, which ranks 5th on the Shanghai's ranking, is well known (apparently they employ some very dubious practices). But Pierre and Marie Curie University for example is ranked 5th in the world by Shanghai, and is not even in the top 50 in the QS ranking. So as far as an academic career is concerned, is a post-doc position in this university amazing or terrible?

The situation seems to be similar for american universities. The University of Minnesota ranks 11th in world according to Shanghai, Texas A&amp;M is 14th and  the University of Washington is 18th, but none of these universities are in the top 50 according to the QS ranking. So, for a future academic employer (say in the US), is a post-doc position in Minnesota roughly comparable to such a position in MIT, or not even in the same ballpark? Is the University of Chicago much better than the University of Warwick (as indicated by QS), or is it the other way around? 

I know that the different rankings use very different methodology and are based on different criteria. But I think this is exactly what makes the question meaningful - out of these criteria, which are the most relevant to post-docs?
None of them. At the postdoc level, you should already be familiar with the people and research groups in your field, at least at a basic level. Go where there is someone you want to work with, and maybe a good active research group, irrespective of the ranking of their university. That ranking could have been achieved because the university is great in a completely different research area, or because it has good conditions for students (as a postdoc, you don't care about this). And, as you state yourself, at high detail level many rankings are bullsinaccurate anyway.