When I was in yeshivah, I was taught very clearly that the hierarchy of rabbinic authority was as follows: At the top were Chazal, then came the Rishonim, then the Acharonim, and finally contemporary Gedolim.
Not only did I really believe this, I also really believed that they believed it. And they also really believed that they really believed it.
Over time, it has become increasingly clear to me that, in fact, this hierarchy is not what people follow. They actually completely reverse it.
In anti-rationalist circles, while Chazal are ostensibly the highest rabbinic authority, any inconvenient sayings of Chazal are simply ignored or are wholesale reinterpreted without any regard as to whether this is really what Chazal meant. (Soon, I will be posting an extraordinary statement from a very prominent Acharon who is explicit about disregarding a halachic position of Chazal in favor of contemporary norms.)
With the Rishonim, despite declarations about Rishonim k'malachim and heated opposition to saying that they didn't know elephant physiology, any inconveniently rationalistic sayings of the Rishonim are ignored, banned from study, and/or openly declared a perversion of the correct approach (but, of course they hasten to add incoherently, it was okay for the Rishonim to pervert the correct approach!). Acharonim trump Rishonim every time.
As for the Acharonim, despite endless stories of their unimaginable greatness in Torah and wisdom, their own "inconvenient" opinions are likewise written out of history. Nobody in the yeshivah world is going to be quoting Chassam Sofer on the science of the Rishonim and the value of secular studies (when taught by an appropriate teacher).
Topping Chazal, the Rishonim, and even the Acharonim, are the Gedolim. They tell us what to think; which views of prominent Rishonim and Acharonim are heretical and should be cast aside; how we to force Chazal's words into an appropriate interpretation.
But in fact, even the Gedolim are not at the top of the ladder. For if any of the Gedolim ever say anything inconvenient, they are simply ignored in favor of other Gedolim who are more cooperative; and if they persist with inconvenient statements, then their Gadol license is revoked. Rav Elyashiv has issued all kinds of piskei halachah that you'll never see on posters or in the Yated.
There was a terrific illustration of this in the comments of "Poshiter Yid" (to whom, despite his amazing anti-rationalist stance, I am actually taking a liking; he's entertaining, eloquent, and not particularly hostile). First he said that the Rambam is "kodesh kedoshim" and that the words of the Rishonim were all given at Sinai, but then when confronted with positions of the Rambam that are different from those acceptable to the Gedolim, he claimed that Rambam was wrong, with the proof being that the Gedolim say differently. Later, he gave a wonderful description of how "the Gedolim guide us and tell us how and what to think," but when faced with a statement from Rav Yaakov Kamenetsky that went against his beliefs, he said that Rav Yaakov must have been under the influence of alchohol when he published it (!)
For anti-rationalists, the Gedolim are much more important than the Rishonim. But even the Gedolim are only respected and followed insofar as their views concord with what the anti-rationalist himself considers legitimate. Amazingly, the hierarchy of rabbinic authority that they loudly claim to be true, is the complete opposite of the one that they actually follow.