Haven't read much of either (Court of Owls and Zero Year for Snyder, War of Jokes and Riddles for King), so I can't make a great comparison, but...
Court of Owls is pretty good, and I can see how people love it, but it seems over-hyped to me. The Court of Owls is a great idea like R'as al Ghul and I hope over the decades to come that whole idea and concept enriches the mythos, but the ending always rankled me in that you needed to get City of Owls or whatever to finish it. Court always felt incomplete by itself.
Zero Year is a mixed situation. Secret City with the Red Hood is one of my favorite stories in my limited collection, and I prefer it over The Killing Joke as an origin for the Joker (before you get out the torches, I do love this story dearly, but for a multiple choice Joker origin Zero Year - Secret City is more epic), and over Year One for Batman (before you get out the pitchforks, I do consider Year One the better story, but it works better as a Jim Gordon origin than as Batman's). Plus the updated version of Batman's original purple gloves costume is pretty neat. And I loved how Riddler came across during Secret City and made me super excited to read his half of Zero Year...but that's where it gets less good. Dark City and Savage City never quite reach the same height as the first entry of the arc. It was still a fun ride though and parts of it were pretty cool, but felt a bit like a letdown after the first part. I should reread it soon and see how I feel about it years later.
Zero Year actually reminds me of Earth One in a way - both got me really excited for a great modern Riddler introduction story, and neither quite delivered what I was hoping for.
War of Jokes and Riddles is also a bit of a mixed bag too, albeit in different ways. I certainly understand the criticism that they tell us rather than show us why this gang war is so bad, when really I wanted to see more of the violence on the streets and the consequences and collateral damage to Gotham. People keep saying that the original plan was for 12 issues, and I think it could have been better with more room for the war to really breathe. That said, there is really some good stuff here. I loved the dialogue, how Joker and Riddler traded jokes and riddles to cut one another down verbally was fun! This story actually managed to make you like and root for Kite Man of all people, while still very much keeping him a joke villain and making that okay. The Riddler actually felt like an A lister level threat alongside the Joker unlike Zero Year while making him mostly live up to that smartest man in the room bit he believes that he is. And I know some fans complain whenever Deathstroke appears outside his rivalry/deviltry with Dick, but it works here because this is pre-Robin. There's no reason to believe in all his years as a criminal mercenary before the Teen Titans he couldn't have come into conflict with Batman or other heroes. I even thought Batman trying to kill the Riddler for killing Kite Man's kid just for a scheme to prove how smart he is really worked, and the Joker stopped Batman from doing it (why?)!
In conclusion, both writers have given me stories that are flawed yet ultimately fun. But if I have to choose between the two, I give Snyder and Zero Year the clear edge over King and the War of Jokes and Riddles, but from what I've read I really don't understand the hate either gets.