Have both, loved both, although I loved the mythology on GoW, I would've loved to have a better in-depth story about the Umbran Witch's mythology if there ever was one, like how she got those huge-as.s summons and how they were dragged to hell, yeah they have cards/info but that's just shallow for me, but overall they are both awesome hack n slash games.

But to OP's question, I think Nintendo just wants to show fans that they can have mature games, don't know if they are competing though, but that's not an issue for me.

I think it's their answer to the people who say that there's no "mature" games on their consoles

Bayonetta was suppose to be Nintendo's answer to; "we have more games other than Mario and isn't kiddish"

I mean, the story for my taste is good and interesting. Greek mythology is fascinating but it's not exactly spectacular. It's a vengence story, we have seen it tons of times, probably with less blood and dismemberment though. If somebody thinks it is a masterpiece, who are we to tell them otherwise, anyways? 

I don't think it's the answer, beat them up games are not exactly uncommon. I do like Bayo's combat better though.

No.

Bayonetta 2 was Nintendo's answer to the lack of games in general for Wii U. PlatinumGames' title was cheap to get and also good. Nintendo didn't have anything to lose.

 I wonder who told you that. Its just a videogame that tells the brutal alternate universe story of a new protagonist based off of the inspiration of heracles. The storyline is cohesive no matter which way anyone likes to slice it. Sure, Kratos isnt charismatic, but he doesn't need to be. Wolverine was an anti-hero and everyone loved hm in the 90's and early 00's even though he had not a shred of Charisma. In his story you know what happened to him, why he goes to fight, who he needs to fight on his mission and who he is facing along the way. You can take guesses at who in Greek mythology he'll face (if you're read up enough on it) and go after them too, because trust me...the real story was more blood thirsty than god of war. Kratos flooded the world for revenge (by mudering the gods he tipped the scales of balance in nature by having no one control it), but Zeus did it because he saw human beings involving themselves in cannibalism and became enraged because he went through that with his brothers and sisters at the hands of Kronos.I really don't see how one is better than the other ultimately because Zeus consumed his own first wife no different than his father consumed his brother, so its all hypocrisy.God of War doesn't need to be a great story, but its presented as brutal as the real one was in an alternate universe kind of way and its fun for me to see the characters get pitted against one another.

The role of Kratos isnt to be intelligent, kind nor fight for what is right. Thanks to God of War with its proper presentation that Dantes Inferno and Star Wars the force unleashed ripped its style.

Okay...then why are you arguing that God of War has a great story? Sure, its lore is cool, greek mythology is wonderful and the set pieces are awesome...but the story past the first game is boring and Kratos is not a quality character. I'll post this video again, as it does a good job explaining how the game's story just fell apart and how the character of Kratos disolved into ridiculous parody: https://www.youtube.com/watch?v=BtgA6SaHHa0

Beat em ups are fast, meter-based combat games where weaponry is secondary to your fists or feet. Its a brawler. Hack N Slash is a similar concept but weapons are the primary mode of attacking your enemies in said game. You don't fight people bare handed in those. They come from a common style but are fundamentally separate in that way.

Beat em up: God Hand, Streets of Rage, Fighting Force, Scott Pilgrim, Double Dragon, Battletoads,

Hack n slash: Golden Axe, Devil May Cry, God of War, Ninja Turtles, Heavenly Sword, Bayonetta, Star Wars TFU, Dantes Inferno

Beat em ups gave birth to the fighting game genre, but the closest two games that are depict what they are all about are known as brawlers such as Super Smash bros or Powerstone. The fighting game genre evolve beyond simple brawlers. 

I never said it was great, I said if you've read greek mythology, its not far off in how brutal things really were in God of War. Kratos was better off dead if he wasnt of use to his father (which is why Zeus tried to kill him in part two). You say to yourself..."Would Zeus really do this?" and the answer would be "yes, he would.". This is why I can accept the events in the alternate universe they've created. The whole thing was an allegory for the world we live in wrapped up in betrayl, fear, lies,  incest, murder and mayhem caused by a governing family that everyone feared but respected because they held up the balance of life. Its basically a soap opera with superpowered beings and a god that couldn't keep his **** in his pants and the falling out of everything their struggles for power, was always collateral damage.

Even in the video you sent me, it even admitted that God of War meets the requirements of the three elements that are usual in a greek tragedy. It doesnt matter how it comes off to anyone outside of the fact that it set the bar for how the trilogy would play it. No one promised lord of the rings. Its greek mythology.