Unlike other people, I found the story in the TLoU very cliche, while the atmosphere and gameplay was very very very very good. Add in there Joel and Ellie as an iconic couple.

And what else can I say about BotW.

Is zeldas story not just as cliche as TLOU? 

Now you got my attention. How do you suggest then, that Link takes down Joel and Ellie.

Breath of the Wild's story was just as, if not more cliche. The weakest aspect of the game in my view.

Breath of the Wild is not sized up for it's story in the same way The Last of Us is ... let's be honest, a Naughty Dog game with a mediocre story is a huge blow, a Nintendo game with a mediocre story is expected. 

I personally think that The Last of Us has a great story despite the fact that I don't view it as very innovative.

This doesn't say much. Competition was Mario Odyssey in 2017. I would also add HZD to that but I think it was a much harder decision between the first two. I don't think RDR2 had that much of an impact on being groundbreaking (as goty pick) in the sense that it was different from the previous iteration like GoW4 was for the franchise and BotW vice versa.

I also think I can see what OP is trying to say, at least in a general sense, with these games representing the philosophies of the companies in their own respective ways.

It's all a matter of preference. Some people prefer story, some prefer gameplay, some want a mix of both.

I played The Last of Us and found it to be really boring for the first hour (After the intro part, of course), since it was just walking. When the game part finally happened, it was really good for like five hours, but then just started to recycle the same situations over and over. Evade Clickers, shoot runners, shoot people. Insert one-off sequence like the sniper or the tank. Story was cliche, but done well. There's nothing wrong with cliches if effort is put into them.

Breath of the Wild certainly has some problems in the variety department, too. Too few enemy types. Not enough variation in the different areas. But, the physics of the game open it up to a lot more crazy situations and emergent gameplay. However, people who play games for story basically look around and go, "Why am I doing this?" because there's nothing there for them. They want clear goals and characters they can connect with to help drive them onward.

It is an interesting difference in approach when you think about it.

Those giving the awards disagree because RDR2 has received a huge number of GOTY picks. It must be one of the highest second places ever along with GTA V which was beaten by TLOU. 

I think it's more a matter of story being front and centre in TLoU while BOTW prioritizes exploration and mechanical experimentation. Story tends to be the steak in Sony's first party efforts while in Nintendo's its the side garnish.

BOTW's design philosophy is not just an iteration of previous games though, its a complete overhaul that plays unlike anything Nintendo has made before.