This summer, I decided to pick up the book series on which the show is based. I just finished reading it this weekend, and I have to say that it is even better than the show. To be clear, the show is still fantastic; it's just that the books take the experience to an entirely different level.
I was also surprised by many of the changes that were made for the TV series. Certainly, they condensed the dialogue and created more dramatic tension, but they also added entirely new story arcs, creating new characters while cutting others. In some ways, the TV series plays out like an alternative, if parallel, universe to the books.
The books do have the edge in that they complete the story while the TV series ended with its sixth season. It's almost as though the producers were saying that people need to read the books if they want the whole tale. There are certainly some teasers left in that final TV season that made me glad that I was already reading the books.
I recommend both. However, I feel that--as confusing as it might be--it is better to watch the TV series first, then read the books. Otherwise, what I feel is a great TV series could feel like a bit of a let down.