In my opinion, The Last of us seems like a superior game. Not that Bioshock infinite is a bad game, but TLOU expresses a whole lot more of a dramatic and emotional story. In addition, the graphics are amazing and both the events and the designs of the game are realistic. While an outbreak of a cordyceps brain disease is not contagious to humans, the game expresses a series of wide-ranging events that stimulate what would really happen during a situation like this. On the other hand Bioshock Infinite has much of a less realistic setting, giving it a fantasy-like story instead of an exciting play through like TLOU does. Yes, while a floating city like Columbia is possible, it's mood is too fantasy-like. Again, this is an opinion.
I am a lover of both of these games. They are two of my favorite games of all time in fact. However, we must consider that since Infinite has no multiplayer(because it doesn't need it anyways) we can only compare the stories to make this a fair argument. Infinite has a fantastic, creative new world to explore that hasn't been seen in modern media, executed this greatly. The fantastic voice acting and art style, and the great story and twists make this game better, to me. After I beat this game, I needed to take a long walk to contemplate what I just played. I did not need to do this with the Last of Us. The ending of TLOU was made to ensure it could have a sequel. It was all that good of an ending, and the story has been done before and is really overused today with zombie-esque apocalypses, everywhere. I'm not trying to say the art and voice acting in this game is bad either. It's actually quite good. I simply like Infinite's better. Also, the Burial at Sea DLCs are very fun and just add to the story. Actual necessary and worthwhile DLC? Not something you see everyday, nowadays.
Let's just all recognize that both of these games are absolute masterpieces though, and both deserve to be ranked in the upper echelon of games, no doubt.