I'll summarise the franchise's history, since there's lots of it. Godzilla is a fairly boring film series with one standout brilliant entry (the 1954 original) and an awful lot of pointless monster flicks. I have fond memories of the Hanna-Barbera cartoon, though. Personally I don't think Godzilla is a drama-friendly format. A Godzilla film will contain: (a) giant monsters smashing stuff up, and (b) humans trying to do something about (a), which is basically impossible and tends to pull the film towards generic government/military conversations with no human content.
This is the 29th Japanese Godzilla film (i.e. not counting the 1998 and 2014 Hollywood ones) and the third time Toho had rebooted the series after putting it to rest for a while. Both of the Hollywood films had been extremely profitable. (Yes, even the much-derided Devlin/Emmerich one, although the studio had expected more.) The 2014 one made over half a billion dollars from a $160m budget, but this 2016 one was actually a better return on investment. Budget: $15m, although you'd never guess and the special effects are great. This Godzilla does some awesome stomping. Total international box office: $78m.
In other words, it's one of the two defining Japanese films of 2016, the other being Your Name. Tomoko thought it was good, but she didn't see why it had been such a hit. I more or less agree.
The important thing it gets right is to do something rare and special in Godzilla films, which is to have a theme and be meaningful. It's portraying an Act of God on a par with the 2011 earthquake, tsunami and Fukushima Daiichi nuclear disaster and examining the official response to it. There are ministers with foresight, but they have plenty of colleagues who are less blessed. Our hero, Yaguchi (Hiroki Hasegawa) assembles a team of eccentrics and misfits to find insights that they hadn't been getting from more esteemed but cautious academics. There's discussion of when and how much to tell the public, showing that monster movies have moved on since the 1950s. The military is careful about whether or not their actions would cause civilian casualties, with an offensive at one point being halted while they wait for an evacuation to be completed.
There's international awareness. America is pushy and kind of irritating, although I don't think they take it all the way into America-bashing. (There are plenty of films out there that do go that far, but this isn't one of them. I found its right-wing sentiments more noticeable, with the caveat that "right-wing" means something different and more nationalistic in Japan. "Post-war is a tributary state. Post-war lasts forever." The film also approves loudly of Japan's armed forces, but that might be inescapable in a monster movie like this.) When the USA decides to drop nukes, it's hard to deny that they're making the right objective choice, even if the film also has a Japanese perspective on this. There are some quick shots of the Hiroshima Peace Memorial.
This is a film that considers the economic consequences of being attacked by Godzilla. It has footage of food lines and of people in emergency shelters. All that it's doing pretty thoroughly.
What's more forgettable is the human cast. They're the film's focus, with the big lizard himself getting relatively little screen time, but even so they're fairly generic. Hiroki Hasegawa is the Good Bureaucrat. Satomi Ishihara is the faintly annoying girl who's the Special Envoy for the President of the United States and should just stop talking English. Please. I'm not objecting to her pronunciation, which is naturalistic except when she's got to say a whole lot at once, but it's more the character's use of English that I found annoying. (I disliked Ishihara in the live-action Attack on Titan films too.) It was nice to see Ren Osugi again as the PM, but there's not much characterisation here on a subtler level than people doing their jobs.
Godzilla him/herself is pretty cool, though. (S)he has more than one form, with the first one we see properly being a slightly comedic thing that you could imagine being made by the BBC for Doctor Who. You won't see that one on publicity materials, but you can see adorable fan art by doing a Google image search for "Kamata-kun". (S)he also has superpowers. Imagine Superman, but bigger and uglier. It probably helped that this is a fairly talky film in which Godzilla isn't usually the focus, which will have allowed a more focused use of budget.
The film also has interesting directors. Hideaki Anno (Neon Genesis Evangelion) was a fascinating choice for writer/director, but he brought in his old friend Shinji Higuchi as co-director. This is alarming. I've seen his live-action Attack on Titan debacles and I know the reputation of his 2007 remake of Japan Sinks. Fortunately, though, the film survives him. I suspect Anno wanted him because he's one of Japan's top special effects supervisors, which is a good reason for this project.
It's a very Japanese Godzilla film, after the triumphantly successful but American 2014 one. It's going back to the franchise's roots, with no rival monsters and no Godzilla vs. Something-ra punch-ups. It's using Akira Ifukube's iconic 1954 music and even the original 1954 roar. (Yes, there's fan debate over Godzilla's different roars.) Given that and its explicit themes addressing a disaster that's still fresh in people's memories, in Japan it's considered one of the franchise's best films and even won best picture at the Japanese Academy Awards. Personally I think that's loopy. It's not brilliant, but it's reasonably good despite being a Godzilla film. That's about as far as I'd go, since even saying "reasonably good" needs you to be not uncharitably disposed towards it.