Michael Quinn’s review published on Letterboxd:
This immediately became one of my favorite things. It's directed by Hideaki Anno, the creator of Neon Genesis Evangelion, which I am an enormous fan of. And once you think about it, he's a natural choice to helm a live-action kaiju film as many elements of Evangelion, most especially the Angels, draw on the kaiju tradition. And Anno nails it. Shin Godzilla uses all of the best elements of Evangelion: the military action, the well-developed politics, and the soundtrack. Oh yes, the soundtrack. I felt such deep and profound happiness when I heard the chords of Evangelion in a Godzilla movie. Getting the best of both worlds, the soundtrack also has many references to original Godzilla movies.
Anno also had to good sense to put aside elements of Evangelion that would've had no place here: the metaphysics, postmodern elements, and explorations of depression (there are no whiny Shinji-like characters to be found). The movie also follows in the tradition of the original 1954 movie by having deep political messages, running the gambit from the slowness of Japan's consensus-based government bureaucracy, to U.S.-Japan relations, and of course nuclear weapons. Due in large part to these modern political themes, and Anno's direction, the movie feels surprisingly realistic for a movie about a giant atomic lizard monster.
There are flaws. The final method of combating Godzilla looks a little silly (I don't want to go into too much detail for spoilers), and the end comes rather suddenly. These are minor, however, especially in light of how fun everything else is. Frankly, Shin Godzilla makes 2014's Godzilla look like garbage by comparison (and I liked that movie!).
P.S. After writing this review, I discovered that I had watched a 100 minute cut of the movie, while the theatrical is 120 minutes. This is upsetting, but on the other hand, I get 20 extra minutes once my Blu-Ray arrives! Hopefully I'll just end up liking it more!