OP, you're asking the wrong question in a lot of respects. Put simply, ignore "prestige" unless you want to spend your career maximizing your ability to flatter yourself at cocktail parties. Your reference to "top 20 biglaw" (whatever that means) makes you sound like that kind of person; if that's the case, then take whatever appellate clerkship you get, stop reading, and enjoy a lifetime of striving.
Are you a practitioner or a law student? Prestige definitely matters in practice because it affects your hiring prospects, the respect accorded you in the firm setting, the weight given to your opinions, and the degree to which powerful people in the firm will seek to befriend you or ignore you.
Your "ranking" request completely misunderstands this. For example, the whole concept of "circuit prestige," like the concept of "Vault prestige," is an invention of insecure law students. No one who matters thinks that way. That's because the degree to which a clerkship is respected depends almost entirely on the particular judge, not the court.
I beg to differ strongly on this one because frankly, splitting hairs on which obscure judge within which Circuit is better than another obscure judge is the domain of law students. Most firms know the most famous judges whose names are nationally admired (Posner, Easterbrook, and a few others) and the judges on the particular Circuit the firms are located in or practice in front of most often. The rest of the judges in the nation are obscure. So, I ask about Circuit prestige precisely because most practitioners know Circuits and Circuit reputations, not judges. The purpose of this thread is to conduct an informal poll in Circuit reputations.
Having said that, it's true that because appellate clerkships are more competitive, having one under your belt sends a signal that 1) your credentials were sufficient to land you a highly coveted position and 2) you got experience with a very bright judge working on complex and/or novel legal issues. For that reason, an appellate clerkship has become a de facto requirement for many AUSA positions and most academic positions--it signals to others that you're smart and got unique, valuable experience, maybe even more so if you end up clerking for a particularly respected judge. But again, it all depends on what you want out of a clerkship.
This is helpful. Thank you.