What is so great about this movie?

Besides no shot wasted, every moment loaded with meaning, first class world building, amazing long shots, and basically doing everything the right way. It is the subtlety of it. It never turns into an over the top dystopia. It is a subtle bleakness that makes it so engaging and believable.

My favorite all time move is Lord of the Rings. The best movie I've ever seen is Children of Men.

Nothing. I think people like it because it is pro-(illegal/irregular)migrant propaganda and it was kind of ahead of its time in pushing that agenda. The 'good guys' are lefties, the bad guys are 'nazis', that's really the intellectual depth of the film. There's not much else to say about it.

Zilch. The storyline is so ridiculous as well as the whole script. The only redeeming value is it has some good actors and tries to create a dystopian world with dark lighting, etc. I mean when Clive Owen said, "I've got to take the day off because I feel so bad about the death of the 18-year-old superstar" (who is only a superstar because of his age), I knew what to expect for the rest of the film and its mediocrity did not disappoint. Once the great Michael Caine had to stoop to lines like, "look at my finger" it lost me for good.

You pretty much answered your own question when you gave your two cents on The Lighthouse. You're just not an art guy.

I saw it in theaters and was blown away at the time. The 8 minute single take action sequences, the familiar dystopian society that resembled certain post-9/11 world, everything on screen appeared fresh and relevant. It even seemed prescient a few years later with the refugee crisis and Brexit.
But on closer inspection the movie is a little under and conveniently written for the main characters to get out of insane situations relatively unharmed, or unanswered logical question - eg how or why the Army just let the only child anyone had seen in decades walk away from a war zone at the end.

I agree that the idea of imminent human extinction in such a banal manner is existentially depressing and incredibly interesting to see people react to, but it feels like the world isn’t explored enough by the filmmakers. I used to rate it quite highly, but these days I would lower it down to the 7 or even 6 range as okay to pretty good. By comparison, I would probably rate Cuarón’s last movie, Y Tu Mamá También, a lot higher.