I recall an NPC, a bearded man, who gives Link an apple of some sort. This occurred during the treehouse demo.

Hmm, I'd argue the real world features wildlife living farther apart from each other than how they are shown in Horizon.

Please don't mistake this as me saying LoZ is the superior game or something, I don't feel that way at all. Neither of these games are yet to release.

Why are these being compared? They're not that similar! I'm excited for both. The Zelda series is my favorite game series of all time, so personally, I'm more interested in Zelda. That said,
1. Horizon has more "new" stuff. Everything new in Breath of the Wild isn't new in gaming, it's just new in Zelda. Horizon has a female lead (not new, but still very rare in games) and so far, every living thing we've seen that isn't human or plant is a robot. Never seen that in game. Hence, Horizon is more unique.
2. Horizon has better realistic graphics, but Zelda has one of the best toon graphics I've ever seen, right next to Appleseed Ex Machina, 009 Re: Cyborg and CrackDown3. The explosions are more gorgeous than realistic explosions (maybe because I've realistic too many times) in the eye of this beholder. Art style is probably the only area where Zelda is more unique.
3. Anyone that has played Zelda knows how puzzle heavy it will be. They've told us there are over a 100 shrines (read: micro and mini dungeons), and if there's about 9 dungeons like there usually is, that's a lot of puzzling. Horizon's combat is bound to be deeper and more fleshed out than Zelda's. It's made by Guerrila games.
4. Horizon will have a better story, better cutscenes and probably will be fully voice acted. Zelda will probably have voice acted cut scenes, since we heard an audible voice wake Link up at the start of the game. VERY DIFFERENT GAMES!
I'm still not sure why we're comparing them. Is it because they're both open world and feature a protagonist that can wield a bow? I want to play both for very different reasons, and I'll genuinely be extremely surprised if Horizon is a better game than Zelda (not by my fanboy opinions, but by the opinion of the majority of gamers and critics). That won't stop me from playing Horizon. Why exactly are we comparing them again?

Ok but come on. They streamed the game for what? 5 hours? And all we saw was 1 person? We've only seen Horizon for a total of 15 minutes. This game is like the Witcher 3, there will be towns and a bunch of NPCs in which we get quests from.

Well it doesn't matter about the real world, these are video games. And we're talking about what it makes the game feel alive. If everywhere you go, you see Robot dinosaurs, I would say it's alive.

There were 8: The old man, four Shiekah for each shrine, and three or so Koroks. 

Plus they mentioned that they were avoiding towns for story reasons. So... 

They both look great, but I'd have to go with Zelda. Being able to do these things for the first time in a Zelda game is way more intriguing to me due to the games lore than Horizon

I will be getting both games, got the collectors for horizon preordered :D

I can't attest to all five hours but at the same time, I'm not claiming the game will be filled to the brim with NPCs. I play LoZ for minigames and puzzles, big and small, so I'm good with a moderate amount of NPCs as long as they're interesting.

As a matter of fact, I'm skeptical of this new direction. I'm old-fashioned: I want my dungeons, I want my gadgets and gizmos for those dungeons. Hoping the game can deliver in this respect.

Let's reserve such a judgement until after Horizon has released.

Just trying to establish there's more than one way to make a game feel alive.

As a matter of fact, I'm skeptical of this new direction. I'm old-fashioned: I want my dungeons, I want my gadgets and gizmos for those dungeons. Hoping the game can deliver in this respect.

Have you checked out the dungeon gameplay? They said it'll have 100 mini dungeons that are focused on puzzles and it has those gadgets so I wouldn't be worried.

Let's reserve such a judgement until after Horizon has released.

Well I don't doubt that the game will have towns and quests, but for whether it's good, yes we'll have to wait.

"Just trying to establish there's more than one way to make a game feel alive."

Yeah but I guess I'm just saying what makes a game feel alive for me, and of course we all have different opinions. I find that Zelda is somewhere between a dense open world like Witcher 3 where the maps aren't really big, just packed and open open world like Just Cause 3 where it has a huge map that really isn't dense.

Horizon look far better in visuals, game world, uniqueness and realistic. Zelda open world looks like last gen and has gameplay elements of retro style which is not realistic but I agree its fun to play. For me, its horizon which has wow factor as its trying to be realistic, has complex and new gamplay style which requires strategy and more story focused so far what we have seen, where zelda is not.

EDIT:

One thing I see from many people who voted for Zelda are going blindly and biased that it will be a better game as its trying new which has not dong before in Zelda and has showed more gameplay elements in the trailer which is actually not somethign new and they just applied retro gameplay in open world game and its kind of disconnecting me due to not being realistic.

Horizon is a realistic looking videogame. Zelda BotW is art, a journey, a dream.

Horizon is realistic? What world are you living in. How isn't Horizon a art, a journey, or a dream? Horizon has built an amazing world, with a very interesting story.