BOTW's story works a lot better than TOTK's story because of the difference in their driving questions.
For BOTW, the main question you ask from the start is "Who am I?" and also "What happened to Hyrule?" You learn the answers to these questions over time as you journey across the land and remember things about your past. The answer to "who am I" is "I am the chosen hero," and the answer to "what happened" is "We failed to save everyone." When you learn that, the goal changes from "go and do the quests because the old lady said to" to "Do what you couldn't do back then and save everyone."
In TOTK, the question is "Where the heck is Zelda?" and it's not your question, it's everyone else's. All the NPCs want to know where she is and you're just kind of standing there while everyone discusses it. And then the game throws you an early game side quest where they tell you exactly what happened to Zelda, and then you just have to putter around for 99 years and watch everyone run blindly towards Fake Zelda while you just follow them without saying anything until the final hour.
And then they force you to listen to the exact same spiel about the Imprisoning War, 4 separate times, without changing a single word. Whereas in BOTW, you get to learn about the Champions and who they were and their relationship to you, and explain the Calamity to you in one cutscene.
Plus, they don't expand on anything from BOTW in TOTK. Link and Zelda are just living perfectly fine in society despite having basically been dead for a century. And instead of expanding on the Sheika mythos, they just try and pretend they never existed and put the Zonai in their place as the Ancient Precursor Race with all the Ancient Technology That's Been Lost To Time.
So yeah, I'm a little bit disappointed in the story of TOTK. BOTW had an interesting narrative that meshed well with the open world format and was executed perfectly. TOTK just had an excuse plot with no substance.
