They beat the **** out of each other strategically.
On the remake aspects of WWHD, I think that it isn't really all that better than the gamecube version from what I can see. Lots of environments and interactable objects in the world are still really low poly, which seems lazy, because the characters and enemies look great. I get camera clipping issues a lot when indoors, where I can see outside of walls into the blue void. The swift sail makes sailing brain dead easy, which maybe I'm taking for granted, but I got it so early (first night time on Windfall) that it doesn't feel special or earned as an item.
Skyward Sword was good because the dungeons and environments leading up to them had the best puzzles and interactions. Enemies also were far more dynamic than ever, and they were just as much puzzles and parts of the environments as everything else. People might criticize Skywards Sword for slow and boring dowsing, but in reality everything is faster. I can run up ledges instead of a slow climb. I can sprint. This was super noticeable to me when I was in the sacred haven and was opening chests that were only accessible by gliding with the deku leaf. Climbing to the top of the Haven 5 times made me realize how long it takes Link to pull himself up off a ledge. Skyward Sword did that so much better.
Also the fact that I stopped using treasure charts because I don't want to waste money due to wallet limit. In Skyward I constantly had an unmaxed wallet until the end of the game.