I like both Nolan and Snyder. There very similar in that each has a limited bag of tricks, but those tricks are amazing (their technical skills, the strength of their compositions, distinctive visual styles, etc.). They both can make films where critical elements are missing -- like decent dialogue in Tenet -- and it doesn't really matter.
Their biggest difference might be Snyder's got a somewhat underserved bad reputation and Nolan a somewhat undeserved good one.
Oof. No.
Sometime I jump on the "make fun of Zack Snyder" memetrain, mostly because it's funny, but he's a successful and accomplished director. That said, he's no Nolan. He's not even in the same conversation.
In the most favorable light, Snyder is Guy Ritchie. A director who broke out by having a visually inventive style (he directed
Lock, Stock, and Two Smoking Barrels along with
Snatch), was way overhyped, and later turned out to be a perfectly good director once he moved past the early stages ... I still think that
The Man From U.N.C.L.E. was criminally underrated.
The best (and worst) thing that ever happened to Snyder, on the other hand, is the unexpected success of
300. Whether you think it's a masterpiece of inventive filmmaking, a paean to Miller's barely-hidden neo-fascism, or both, he has continued to go to that same well (color palette, slow-mo, pacing issues making everything go to 11, Manichean conflict/shots) over and over again with diminishing returns. I don't want to say this as a back-handed compliment- in much the same way that people "mock" one-hit wonders in music without realizing that even being a "one-hit wonder" means that a band was more successful than 99.99% of all musicians, ever, I can say that Zack Snyder is a good director, a distinctive (if limited) visual stylist, and someone that can manage a major Hollywood Production (which is no small thing). But he's not a great, or subtle, or "artsy" director. He's a visual stylist, who can be a little one-note, who loves comic books and genre works. That's not a bad thing.
Which is not true of Nolan. Yes, there are certain things that you often find in most Nolan movies- a Hans Zimmer score. Michael Caine. Tom Hardy. The plot unfolding in a strange manner (often with some element of a "puzzle," that usually involves time in some fashion). A meta-element, wherein the film elements (including the score) and the plot itself in someway reflect each other.
But the movies themselves are usually quite different visually and thematically; it's not like he's Wes Anderson with an easily parodied style. Dunkirk is not Interstellar is not Inception is not The Prestige is not Memento; while each of them use different techniques, they are, quite clearly, a WW2 Film; a post-apocalyptic meditation on love, loss, and sacrifice; a mind-bending thriller; a period piece about truth, deception, and art; and a B&W 'art' film that is a shocking 'M. Night' twist-y puzzlebox.
In other words- very different directors.