This is definitely closer to Uncharted 4 than Breath of the Wild -- at least for the first several hours.
I haven't made it super far into the game, but early on you're not really allowed to explore the world. It's very linear and scripted, but the game itself is sorta blended with the "movie" aspects, so it has a nice seamlessness style with it.
An apt comparison to Zelda games, though, is all the puzzles. It's all very environmental and blended into the scenery, and you have to solve the puzzles to move forward through the world kind of like a permanent zelda dungeon.
The only awkward part -- besides the sorta painfully obvious tropes -- is how there's so much restriction to go along with the story. Again, I don't know if this is only the first portion of the game, and I just haven't made it to where things open up further ... but it reminds me so far of being like a much much much more restricted version of "Horizon: Zero Dawn". That too has an early story part, and of course Breath of the Wild has the plateau, but they're really just restricted portions of the game that teach the mechanics. God of War, though, feels like it's restricting sooooo much so that you can follow along the story -- a lot more like an Uncharted kind of game. You basically follow a super limited path until you get to an open-ish area, and then that area turns into a big fight arena, you beat the baddies or maybe fight a boss or mini boss, and then you move forward with some puzzles and bonuses if you're willing to explore and look for stuff on the side ... but if you look around toooo much, you'll find that there's basically nothing in most places.
I'm still early in the game, and it gives the impression that the game opens up and places become areas to return to and go through again, but I haven't seen any of that yet, and with the amount of time I've put in so far, games like "Horizon: Zero Dawn" and "Breath of the Wild" would have already opened up to the "open world" aspect.
Basically, it's like an Uncharted version of "Horizon: Zero Dawn" that's promising the open world freedom and side missions and things, but maybe it's just a different kind of balance between freedom and story, and this is just leaning more towards story.
The axe is super friggin' dope, though, and playing on harder difficulties really requires you to coordinate a LOT to deal with even just 2, let alone 15 baddies at the same time. Especially as you have like flaming rock throwing monsters on ledges and crazy shielded monsters and running around hyper monsters, and it's just like 20 things happening at once, which is awesome. It's challenging, but it's not infuriating, because it basically comes down to forcing you to act like a movie action hero. You have to toss baddies into other baddies, throw your axe up at the ledge baddie's head then kick the monster in front of you, call your axe back and follow up the kick with a smash, and just power through like it's a crazy coordinated fight scene. It's a really really neat learning curve and style for success.
There are ways to possibly hide or run in and smash and run out, but that's really only possible with the big troll bosses, because it's kinda how they're designed to be fought. For the regular fights, you can't really "cheat", because everyone sorta has a pattern, and you're meant to jump between each type of baddie so that the timing of their attack patterns lines-up with your attacks and you don't get destroyed immediatley. If you try and cheap-shot from a distance, it's like a weird timing thing where you have to wait for the pattern to loop and jump in once every loop. It's possible, but extra extra tedious, and it's basically an indication that you're doing the game wrong. You shoulda planned better and looked cooler.
Super self-contained and not sure how replayable it'd be, if you just rush through games, but it's worth going through it and it seems pretty well stuffed to be worth the playthrough.