Game spoiler: Abby in the game is HENCH and kills Joel by caving in his head with the golf club - show Abby is skinnier so I get why they changed it to her stabbing him with the broken end of it... it somehow seemed even more brutal that way, though. But I guess also saved them from having to create a Pedro Pascal prosthetic with a bashed-in head

. A "cleaner" death, in that sense.
Also it was interesting that they divided the characters up differently. Game differences:
It's Ellie and Dina on patrol together, not Ellie and Jessie.
Joel is on patrol with Tommy.
That scene is otherwise the same (Tommy in Dina's place) except that he gets hit in the head and knocked out, rather than injected with anaesthetic.
Dina and Jessie together find Ellie and knocked-out Tommy in the aftermath.
The attack on Jackson doesn't happen at all.
I actually understand all of those swaps to be fair - the Jackson attack makes sense because I always wondered where the infected hoard went in the game! After Abby/Joel/Tommy escape from them (and the lodge scene plays out) it just sort of cuts back to Jackson where everything is fine. Other than Joel being dead. Where did all the infected go? Never answered it's never mentioned again

.
Also as they skipped the Joel/Tommy/Abby infected fighting they needed a replacement sequence for action + showing Tommy to have skillz.
There's a much longer sequence of Abby/Joel/Tommy fighting off infected together after Joel saves Abby, which IMO makes the killing more shocking/brutal, as they've been fighting side by side in the lead up to it.
Abby doesn't find out that Joel is Joel until after they get back to the ski lodge when he introduces himself (at which point she kneecaps him with the shotgun same as the show).