During these past years A Song of Ice and Fire has become pretty popular. Many people who didn't like Tolkien due to his endlessly descriptions of surroundings etc have instead liked GRRM's works. I've recently begun to read A Game of Thrones, the first in the A Song of Ice and Fire series (why I haven't read this earlier I don't know). A Game of Thrones is by far a lot easier to read than The Lord of the Rings (or the heavier works such as The Silmarillion, The Children of Húrin, etc) which of course is nice but I think that if I were to chose one book I think I still would pick some of Tolkien's work due to the richness in his language. I'm not saying that GRRM's writing is simple but maybe it's due to the fact that Tolkien wrote his books in another time era. Every time I read his books I learn new words but above all, his words seem to come alive much easier than GRRM's words and the picture Tolkien paints is to me more vivid.
One thing that I think GRRM has done better than Tolkien is the way he makes a character's personality. Tolkiens characters are sometimes a bit plain; Frodo accepted to destroy the Ring and Sam followed his master - there was never so much fuss about it, they just did it. I think GRRM's characters feel more alive, you get to know more sides of them (although it's quite annoying that you never really can determine whether a character is evil or not...).
One thing which I missed in A Game of Thrones is poems. I might have been a bit spoiled by Tolkien's endless amount of songs and poems, but I love them. I love to read them out loud, to feel the power of the words and just to taste the combinations of words and phrases.
I love that Tolkien has made a story which is thrilling - and a bit scary without it being "R" rated or its characters too ruthless. Although I quite liked GRRM's element of horror it's not always what I desire when I want a good fantasy book. Nonetheless, it's a really good book and I'll definately buy the second book, A Clash of Kings.