Spoilers below, beware.
I, overall, prefer Breath of the Wild to Tears of the Kingdom. I am generally drawn towards subversive, isolating and mystery-rich Zelda games (OoA, MM, PH, LA). These are often the sequels to more traditional, but still enjoyable, entries (OoS, OoT, WW, ALttP). BotW and TotK break this trend for me. The isolating nature of BotW's world is just more effective than the communal focus of TotK's world.
- I prefer BotW's combat: I appreciate the customizability of the Fuse system, and can get somewhat on board with cannons, construct heads, homing carts and flame, frost, shock and beam emitters for Ultrahand combat, but there is a simplicity to BotW's combat that I appreciated. Gleeok's are a tremendous new challenge, but I preferred when my combat skills were based on my ability, not my creativity with Fuse.
- I prefer BotW's shrines: Though I like TotK's puzzles more overall, like Moblinking said, the variety of Shrine Quests and shrine puzzles is much greater in BotW. The overworld puzzles in TotK all basically give armor, or aren't really puzzles? There's a couple strong ones in Gerudo, but shrines don't feel like an event like they did in BotW.
- I prefer BotW's map. Not sure why: the caves, Sky, Depths, and environmental changes more than justify the argument that ToK has an objectively better map, but I think it ties into the story: the aftermath of the Upheaval is not nearly as interesting as the aftermath of the Calamity. Which brings me to...
- BotW's story is stronger. The memories create a real sense of "oh, Zelda failed, Link failed, there is very little hope that this gets better and the entire world is in a state of paralysis." In TotK, vague-motivation Ganondorf wants to...darken the world. In BotW, demonic force of nature mindlessly lashes out at an entire kingdom, bringing it into abject ruin. It's just stronger.
- BotW and TotK have basically the same characters, and I love the development for all the minor NPCs and larger characters (Purah/Paya/Tulin/Sidon/Impa) specifically, but Zelda is just such a strong character in the BotW, and TotK doesn't really have anyone filling those shoes. And BotW layed the groundwork for Zelda's strongest stuff in TotK, which is only present in two memories. I love Mineru, Sonia and Rauru but Urbosa, Revali, Daruk and Mipha they are not. And Ganondorf has no Wind Waker motivation: he's just intelligently but mindlessly evil.
- This will be most controversial, but BotW has stronger dungeons. The way the Divine Beasts can be controlled and serve as these mammoth titans of legend and directly impact the past part of the story; the TotK dungeons are all back to generic temples with admittedly unique twists and strong design (the Lightning and Wind temple's especially). But the Water Temple, Spirit Temple, and Hyrule Castle are all weak dungeons, and don't compare to the brilliance of BotW's Hyrule Castle.
- And finally the community atmosphere of TotK is not as strong as the isolating atmosphere of BotW. I initially ranked TotK below Oracle of Ages and Link's Awakening, until I started my first dungeon quest and Tulin just started following me around. I was like, "oh wow, are Tulin, Sidon, Riju and Yunobo going to follow me around all game?" And the answer was no, their weird spirit things would. In BotW, who follows you around? Absolutely no one. Who cares if you live or die? Maybe Impa and Purah (and Paya), maybe. In TotK, the entire world knows you, you are the legendary hero who has already saved Hyrule, it just makes the entire place too familiar but they don't go all the way and allow Link to genuienly feel like that hero. It's stuck in this middle-zone. It's obviously still pretty strong, Lurelin is great, Gerudo Town is great, love Hateno and the domain, but there's not this pervading sense of failure, loss, grief, and isolation.
I think I might be holding a chip on my shoulder about the way the end of TotK completely disappointed me, and also the insane tedium of the new armor upgrades and dragon system, Korok buddies and overworld boss count, but I've sat with TotK for a month now and do think I overall prefer BotW.