I agree with the cartoonishness of Warhammer diminishing it somewhat as a setting. But one has to keep in mind it's all designed for miniatures using "heroic" scale, i.e. hands, heads and stuff like weapons being over-sized, not so much for the aesthetics as for the ease of painting. It's all over the place in a lot of ways, and IMO would be a better setting if the visuals were more grounded in reality and there was a bit more coherence in the world (technology etc).
I would prefer aSoIaF:TW myself. The magic is toned down and wouldn't affect battle gameplay much with the exception of dragons (they would kind of break it though, they're basically the nukes of the setting). It would still make for a very good game with a proper character/politics system. LOTR could be good but the conflict is so one-sided strength wise the good guys' military victories were all just about winning time at the end of the day. An accurate LOTR TW would have to be more of a "survive X turns until the ring can be destroyed".
On an unrelated note, that graph clearly shows Medieval 3 is what most people want. I keep hearing rumors about China TW. Hope that's not the case but that's for another thread.