It's not a case of having waited for it as such, but I played The Last of Us this year, after watching the show. I'd say it was worth it, and I don't mind that a lot of the story beats and emotional moments were 'spoiled' as such, because I still felt them when playing the game.
Apparently some people don't like that you asked that question.
I honestly couldn't say. Usually I'd be able to give you a definite answer one way or another (and maybe my answer would be different if I'd played the game first) but I don't think there's a huge difference. Maybe just go with whatever you get a hold of first?
That said, you can never go wrong with experiencing the source material first; at least not when the adaptation is of a similar quality. You'll have a good experience either way. It really just depends on whether you want to watch the show and say "oh that's how they did that in the show" or play the game second and say "Oh, that's what it was originally like!"