Y'know, comparing Tolkien to George Martin I pick up one big difference between the two. LOTR's central theme is the struggle between good and evil. The characters are fundamentally good or bad. In a couple of cases a good individual like Saruman and Boromir becomes bad, and a bad individual like Gollum shows a flash of goodness. But by and large the great majority of characters have already chosen their fundamental dispositions. The Hobbits, Elves, Dwarves, Rohirrim and the men of Gondor are basically good; the orcs, trolls and uruk-hai are evil (and necessarily so as they cannot repent).
More importantly, the societies of Middle Earth reflect the disposition of their inhabitants: the Shire, Rivendell, Lothlorien, Rohan, Lonely Mountain, Dale and Gondor are realms that uphold and defend the goodness of those who dwell in them. Moria, Mirkwood and Mordor are societies all built on evil. There's no cynicism in LOTR.
In GoT it's different: there are very few uncompromisingly good characters. Virtually everyone is complex, doing good and bad things in a way that makes it impossible to determine which side they're fundamentally on. The few good individuals don't drive the storyline - they're either victims or survivors. None of the kingdoms are especially "good". Their rulers and constitutions uphold a social stability, sometime with brutal force, but there aren't any ideals behind it. People who have ideals either die or become/are evil. GoT is all about cynical power, in which some might wish for a better world but have to stoop to the realities of the times.
I think GoT better reflects contemporary society, that may have good people but does not really stand for anything other than the security of those in power. It's "pragmatic." Problem is that pragmaticism goes with compromise, and compromise dilutes ideals and principles into nothingness. Eventually something has to fill the void.
What I noticed about those first-time reactors to LOTR is that they identified with its lack of cynicism. I don't think people are ambivalent - they choose between good or evil (there's no third choice) and then live out the consequences of their choice (though they can - up to a point - change their minds). LOTR reflects that.