I believe TKAMB is worth advocating for, and even reflecting that worth in our institutions, for example by making one required reading instead of the other. But I can also imagine individual circumstances where ASOIAF is a more important and worthwhile experience for someone.
(Edit: Typo)
There's no easy way of answering that on this kind of medium (an Internet forum). I took two graduate seminars and wrote several papers on it :) But as a primer, I strongly suggest reading Hume's 'Of the standard of taste': http://www.econlib.org/library/LFBooks/Hume/hmMPL23.html
In that essay, he attempts to provide some clear-cut criteria for an objective judgment of art, food, and literature.
(Note that there ARE people that are relativists and they have a somewhat compelling argument. That's perfectly fine. I just don't buy it and I think they're wrong.)
You allude this this when you say "GRRM can't hold a candle to the profound impact Harper Lee has had on American culture as a whole". Obviously your own criteria includes how this work affected America. How objective can this be if it may be assessed entirely differently by a Chinese, Russian or African person, where it may have had little or no discernible influence on their culture?
Leaving that aside, the passages in comparison are actually saying different things. Regardless of who wrote them, 3minus1 should be free to prefer that slightly different definition of courage. The source is irrelevant.