Excellent summary!
I'd also add that LOTR is much more quest based, whereas ASOIAF is not based around a journey, or an object, or a definitive end goal (get rid of the Dark Lord.) It's a snapshot of a period of political upheaval across several continents, and follows the major players in that upheaval. It features magic, dragons and zombies, and more sub-plots than you can shake a stick at. By comparison, LOTR is much more linear.
I personally much prefer Martin's series. It's probably my favourite fantasy series ever, and I've read quite a few of the well-known ones.