Now that the shock and horror of Joel's death in The Last of Us Season 2 has dulled somewhat, a comparison can be made between how the HBO adaptation handled his death and how the game originally intended it to be. Joel's death was the driving event in both the game and the show, but how it came to happen in both is very different.
Considering how important this death is for both the game and the show's story, it is interesting to consider the changes that the HBO show has made. Even though the actual act of killing, performed by Abby, an ex-Firefly seeking revenge for her father's death, is mostly identical in the game to the show, there are some different details.
Here are 3 major ways The Last of Us Season 2 Episode 2 made Joel's death better than the games.
3 ways HBO's The Last of Us made Joel's death better
Joel's death was going to be heartbreaking and enraging, no matter how it came to be. However, the show changed a few things about this turning point in the story, making it better than the video game.
Abby and her group were not a bunch of ruthless villains

The one thing that pissed off the video game players more than anything was how sudden and shocking Joel's death was, not just because it was so soon into the game, but also because the players knew nothing about Abby and her group and their motive behind Joel's death. The group's humanization happened too late and too little, making no dent on the players' hurt and anger.
HBO's The Last of Us changed things in this regard, as Abby and her group had been the focus from the start of Season 2. The fans knew exactly why they were hunting Joel and understood exactly why Abby was burning with a deep need for revenge. Even her group is portrayed as remorseful as they try to convince Abby to turn back and leave. Mel, one of the group members, talks to Dina softly and with remorse and is even seen crying and unable to look when Abby is torturing Joel.
The game also plants seeds of humanity for Abby and her group, but it happens later in the game, which did not work out for most of the players. The show makes sure that the entire group comes off as humane and not ruthless villains.
Dina being the one present for Joel's death instead of Tommy

The biggest change that HBO's The Last of Us made in how Joel's death came to be is the fact that Dina was the one out on patrol with Joel instead of Tommy, like in the source. Joel and Dina's relationship has been much deeper in the show compared to the game. So, the fact that she was the one present when Joel was murdered gives her much more motivation to join Ellie on her way to Seattle to hunt Abby.
In the game, Dina only joins Ellie on her way to Seattle because she is loyal to Ellie, but the show gives her more than just her loyalty as a reason; her love for Joel becomes a driving factor as well.
Ellie being awake after Joel's death

In the game, Ellie is knocked out after being kicked in the face after the group kills Joel, and she wakes up in Jackson. HBO's The Last of Us improves on the game in this scene. Bella Ramsey delivers a heartbreaking and emotional performance, as the audience gets to see Ellie crawling up to Joel and holding his hand, hoping and praying he's alive and will squeeze back. But he doesn't.
Another heartbreaking moment is when they are dragging Joel's body back to Jackson, and Ellie turns back, tearfully looking at his body. Ellie's reaction drives home the reality of Joel's death.
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