Would you like a better story? Yes.
Faster climbing? No.
More interesting world? Yes.
I hope that the emptiness and one dimensional storytelling of BotW is fixed. Don't get me wrong, actually I liked that BotW did not have much content in it's world and had a simple story, as this in fact highlighted the beautiful theme of the game: empty wilderness where things are left as they are and they survive by their own (you see the connection between theme and Link, Zelda and silent princess flower). I really enjoyed the tundra in BotW because its emptiness. I wouldn't change much of BotW. I like it as it is. In case that Nintendo is going use same engine and world as in BotW, Zelda Switch could be like missing element that completes the story of BotW. Now that the Land of Hyrule has recovered from grasp of Canon, Hyrule should be more vivid.
So I hope for next Zelda:
-complex main story. In wind waker I liked that you got to meet Ganondorf several times. When I went to Forsaken Fortress second time, I thought game was ending but I was gladly surprised that it continued. In BotW you got the final objective from the king in the beginning of the game so you knew the big picture of the game almost right from the start. This should be different in next zelda.
-side quests also could be more complex with more interconnections with the world or with the main story. Tarrey town side quest was fun.
-more challenging puzzles and enemies. This is the most important request to me. Although, I haven't played master mode of BotW yet so perhaps this wish is already granted. In BotW I liked lynels. More enemies of that level of challenge please.
-more challenging boss fights.
-Getting resources (rupees, minerals, food) should be harder. Now it was too easy and made the game too easy.
-Some location related performance issues fixed. In kakariko village and in Korok forests there were bad issues in frame rate. Otherwise performance was good.
I want them to keep in:
-Voice acting as it is now. Especially I liked Zelda's voice
-weapon breaking. It was good thing as it forced player to plan and save weapons and to use them carefully.
-Raining.
Anyway, what ever they decide to do, I'm pretty sure that I won't be disappointed.
Edit. forgot to mention that I'd like to hear more memorable soundtrack. Hateno village had nice music. I loved those string instruments.