There are actually a few GoT board games. I only have two of them; Battles of Westeros (starter set) and the Game of Thrones Card game. There is also GoT the Board Game (it focuses on the whole map of the continent and not just single battles.
As for what is best, it depends. The show is good, but they change things and leave out a bit of content. The books are king. The comic adaptations are pretty close to the books.