Symmetrical and asymmetrical models derive from fundamentally different parts of very basic human psychology. Symmetric is primarily about trust, cooperation, socialization and belonging. Asymmetric is primarily about status, competition, individuation and separation.
Humans are hard-wired at very deep biological level to live their lives out as a balancing act between these 2 basic drives, what one sociologist has called "getting ahead and getting along." Both are social drives, not economic or transactional. They may produce economic or transactional benefits, and that may be why they have evolved in a genetic sense (to help survival) but they are not primarily about those psychologically. This is why pure "interest graphs" (people following topics instead of people) that dilute person-to-person connections with a mediating "interest object" are weaker than social graphs. This doesn't mean they are bad. They just have different dynamics (slower, but with better inherent scaling potential if you can just trigger the growth properly). Academic publishing is a strong kind of interest-object graph, since there are mechanisms like double-blind peer reviews that strongly limit the person-to-person connection. In citations, you nearly always cite papers, not people. Wikipedia is another example.
The powerful way to combine the two dynamics is to use "social objects" instead of "interest objects." Social objects catalyze, but do not directly intermediate, human connections. Think of interest objects as interrupting eye contact, while social objects are off to one side... 2 people may meet because they come to look at the social object, but when they decide to look at each other, the social object, unlike a pure interest-object, doesn't get in the way.
So neither is new (small tribes were mostly symmetric, kingdoms had a lot of asymmetry, with the king having a lot of followers he didn't know personally), and neither can replace the other. We need both to exist.
And despite appearances, the superficial symmetry/asymmetry doesn't make platforms purely symmetric/asymmetric. You can play status games on the nominally symmetric Facebook, and you can play "belonging" games on the nominally asymmetric Twitter.
Quora is VERY interesting because it has a strong "interest graph" bias by actively downplaying the author of a question. But they've left the door open to becoming a very finely tuned social object graph, since they have messaging capabilities, are (thankfully) avoiding a leaderboard, and let people see each other. I haven't yet made any true new friends on Quora, but I've already used the messaging system a few times to talk to people in ways I never did on either FB or Twitter.
This tuning between "getting ahead and getting along" is going to be very very tricky for Quora, since there are parts that naturally drive status dynamics/reputation, and parts that naturally drive belonging.