The writing in TW3 is better than Horizon. It has better worldbuilding, more history and many side characters who are really well fleshed out. I actually think Horizon did a really good job in this regard but TW3 is basically best in class.
The quest design isn't really superior, although it's better contextualised with all of that good writing. You'll still be gathering stuff, talking to people, clearing out monsters, following the glowy footprints, etc. It's the same stuff nicely dressed up. My favourite "good grief this game is wasting my fucking time" moment was when you visit a hermit for some information but before he'll talk to you you have to find his goat which has wandered off.
The world design is really good in TW3, and honestly probably my favourite part of the game. I'm not sure how its size compares to Horizon as I haven't finished it yet (probably a fair bit bigger though), but it feels interesting to explore while also being quite realistic. There's plenty to do and it's a rare game in that the scale feels pretty believable - the city Novigrad is an incredible place that feels impeccably designed. There are of course still some instances of odd distances, like you'll have to look for someone who's missing and you'll find the evidence a few hundred meters from their house, but generally it's better than most at this.
The combat in TW3 is shite though. I've played the game overall for about 16 hours I reckon and I've never gotten used to it, as it feels floaty and lacks impact. It's like someone took the serviceable melee combat from Horizon but made a whole game out of it.
I didn't like the menus or interface either. It was vastly superior in Horizon. I constantly felt like my weapons were breaking and I'd invariably have to spend all my money getting them fixed.