Like many of these discussions, the answer wholly depends on the “definition”. So — in one sense AY is correct, “regarding gadlus ba’Torah [t]he opinion of laymen, of frum professionals, or various shul rabbis is immaterial.” It is meaningless for someone who is not a doctor to opine on who the best doctor is — when it comes to medical knowledge and accumen. However, laymen can give opinions on who is the best doctor when it comes to bedside manner, thoroughness, or attentiveness. I do not have the credentials to determine who knows the most Torah etc. But, i dont think Gadol Ha-Dor, as it is used, means the person with the most knowledge. I understand it to mean who is the leader of the generation that cuts across the spectrum. Certainly , Rav Moshe Feinstein fit the bill. Rav Shlomo Zalman Auerbach also came close. I dont think that its clear that there is always such a person at any given time.
My charedi child often gives me a hard time on my not having “emunas chachomim” or whatever phrase you prefer (da’as Torah). My friend went to go see a very well known Rabbi in Israel. My friend is a prominent professional and is — for lack of a better description — right wing modern orthodox. He has neither has a beard or a hat. The Rabbi advised him — if i recall the story — to grow peyot and a beard. Why am I bringing this up — and what does this have to do with Gadol HaDor or Emunas Chachomim? It would seem to me — that if you are going to be the Rabbi of All (the Gadol HaDor) then you have to “earn” (maybe there is a better word) — the acceptance of all. If you dont get the acceptance of all and you dont resonate with the greatest number of people (at least within the Orthodox world), then I think the title is not fitting. And most importantly, if i dont believe that a certain Rov understands me — or understands my world — then I do not think that I would/could accept him (whatever that means) as the Gadol Hador. To that end, Rav Moshe and the Lubavitcher Rebbe apparently both had the ability to understand the world outside their own enclaves.