I'm reading the book (about a quarter through) after watching season 1, and I feel like some small aspects of the storytelling were not properly reflected in the tv series.
Some Examples:
Jon Snow and Tyrion's relationship
Jon Snow and Cat's relationship
Ned's remorse for killing Lady once he discovered that Summer saved Bran's life
Ned and Littlefinger's relationship
Daenerys and Drogo's first time being intimate (the book illustrates the encounter as being far more passionate and seductive)
I still thoroughly enjoyed Season 1 on HBO, but these small tidbits def make the story feel more complete.
My minor complaint about the book is that sometimes the figurative detailing drags and is a bit cumbersome.