It can go either way, sometimes the "producer" label is really just a rubber stamp, and the product is obviously almost 100% the product of the director's vision. And sometimes the exact opposite is true, with the producer heavily or even dominantly influencing the shaping of the project.
Given that Nolan is on this, I am more in agreement that he's probably playing a large role at every level of this. From the brief clips and tone it has zero similarity to the previous Snyder work imho. The hyper-stylized 300 and slightly muted Watchmen I think were the product of trying to get the extreme vivid/stark look of graphic novel style anyway, and most people don't think of Superman in the modern graphic novel sense .. so it looks like they're doing a more realistic vision here.
Nolan is also listed as a writer for the story along with Goyer. Although, when looking at Goyer, he's more of a mixed bag. Goyer has the newer Batman films under his belt (I'm assuming Nolan's brother was on those as well), but he also has some rather
bad movies as well like the newer Ghost Rider movie. Ultimately, I'm just glad that Snyder didn't write it after seeing the abomination that was
Sucker Punch (he wrote that story).
Hopefully, since it's not a comic being directly adapted into a movie, it won't fall prey to the same problems as The Watchmen. It still annoys me how he tried to justify his changes without realizing how they completely destroyed certain parts of the movie. For example, why the fuck does Ozymandias even kill The Comedian
when there's no island? Why does The Comedian go to Moloch balling like a baby
when there's no island? The whole reason why Ozymandias killed The Comedian was because he flew over Ozymandias's super secret island (where he was creating "The Alien") during a mission. Seeing that freaked him out and caused him to see Moloch.
I won't even get into how they ruined Dr. Manhattan.