Being a Playstation exclusive, I've never played the game. Kind of unfortunate because I've heard nothing but good reviews and feedback about it.
The show has been very good though. Television and movies based on video games can be kind of hit or miss (usually miss). Zombie television and movies can be hit or miss too. Combine them and the odds maybe aren't so good, but they pulled it off.
I think the pacing is what does it really well and I credit Craig Mazin for that. With his last big HBO project, Chernobyl, being a mini-series, you don't have the luxury of multiple season to tell a story. You have a couple episodes to develop your characters, make the audience understand them, and tell their story.
Comparing The Last of Us to The Walking Dead, how long did Frank Darabont, Glen Mazzara, and Scott Gimple keep The Governor around? Two entire seasons. In The Last of Us, we have Kathleen for two episodes and then the show moves on. We learn enough to keep the characters interesting and live their story, but not so long that they become tedious.