I really liked it, but it's a bit of a mess. It's based on the latest manga by Sakae Esuno, who did Future Diary. I loved that. This, though, is going significantly further and I should think any viewer is almost guaranteed to find something about it offensive, overdone, unconvincing or horrific. Hurrah! I now want to read the manga, partly because I want to experience Sakae Esuno's original story unfiltered by this anime production.
In some ways, it reads like a dark parody of light novel tropes. It has a misunderstood hero who's scorned by the world, but has superpowers and will become popular with all the girls! There will be superbattles. There are also some, er, less comfortable tropes. However Sakae Esuno is taking all of those genre elements and ratcheting them up to a level that will break them for many viewers.
It also has nothing to do with burgers and fries. An "Order" is a wish. In the universe of "Big Order", wishes can come true. Think about that for a moment. Anyone's wish, with no filters or entry qualifications. You might be a toddler, a racist or a fundamentalist terrorist. Doesn't matter. Your Disney moment is waiting for you! (I think most people only get one wish, since multiple wishes would just turn reality into rubber and it would be impossible to tell any kind of story.) In fairness, this isn't taken to the horrific extremes that I'm already imagining, but you can see the possibilities. Let's start with our hero, Eiji Hoshimiya. He's the most hated man on Earth because he brought down human civilisation and caused billions of deaths. Yes, you read that right. Hatred seems like a understated reaction. His wish caused the Great Destruction. In fairness he was only a child at the time, but already we're going significantly beyond what some viewers will be able to embrace.
Is he a villain? Is he a hero? Again, it's not that simple. Eiji is a major factor in a lot of reviewers hating this show. We've got used to being spoon-fed in our fiction. We get told what to think and how to react. Eiji though is a bunch of contradictory signals, which is liable to get called bad writing.
Greatest mass-murderer in the history of the world = bad.
Seems like a nice, sympathetic person = good.
Wants to help his dying thirteen-year-old sister = good.
Has a superpower called "Bind Dominator" that gives him absolute power over anything and anyone within range (including the laws of physics) and declares his wish to take over the world = hmmmm.
Relationship with sister, as seen in ep.5 = a combination of two anime tropes that even on their own are distressing and disturbing. This is the kind of thing that in real life ends with someone being stabbed to death by a fellow inmate, a few months into their thirty-year jail sentence.
The fact that he remains the hero even after that = terrifying.
Put all that together and you get a protagonist who's wrong in the head. I'm in awe. it makes him an extreme person to think about. However he's still the hero and we're on his side. This suggests that Sakae Esuno is either: (a) broken and horrifically stupid, or (b) playing dark, ironic games with our expectations of storytelling. One should never assume too much in anime, but I reckon it's (b).
I also admire the story. It's taking no prisoners. It's thinking big. Admittedly it's a bit vague about the rules of all this wish-granting, when you might expect a more satisfying story to be precise and well thought out. Occasionally you'll be asking "why" questions. However if you want that, watch Future Diary. That was a twelve-volume manga adapted into a 26-episode TV series, which felt about right. This is a ten-volume manga adapted into a ten-episode TV series, which is a mess. The storytelling is ugly. It's better in the early episodes, but ep.7 onwards was where I was getting itchy at the plot leaps, missing connective tissue and general sense of bad compression. This is a bold story, but the anime is a clumsy telling of it. There are jarring plot jumps between episodes. A pregnancy is unhappened almost without comment or consequences. (It may or may not have been real at the time, but it was certainly a big deal.) Characters go from alive to dead while we weren't looking.
(I've also heard it said that the anime made lots of ill-judged cuts and changes to the manga. I can't vouch for that personally, not yet having read the manga, but I have no trouble believing that Sakae Esuno's version of this was more coherent and logical.)
Tone is inconsistent. I found that quite bracing and I actively enjoyed it, but once again we have a story that seems to be deliberately going out of its way to startle you. Ep.5, for instance, is the sexual episode, but its approach to this is the opposite of unified.
(a) it starts with five minutes of cheap exploitation. All the girls get in the bath (with lots of nipples if you're watching the Blu-ray version) and one of them starts groping the others. It's indistinguishable from every dumb fanservice anime you've ever seen.
(b) then it has the bad thing.
(c) oh, and relationship stuff with the vengeance-driven girl who's been forced to be Eiji's girlfriend even while she's trying repeatedly to kill him. This was played for repeat-fatality comedy in ep.2. (Which was funny, by the way.) If you're reminded of Future Diary's Yuno, then... well, yeah. Yuno was more awesome than Rin, but there are crucial differences between the two that prevent Rin from being just a retread. What's interesting about her, incidentally, is that her hatred of Eiji is rational and sympathetic, while his domination of her is bordering on villainous. I reiterate: he's the story's hero.
If you didn't like Future Diary, avoid this. It's even more of all the things you disliked, plus choppy storytelling. The show's going out of its way to make aggressively questionable decisions, e.g. that outfit on that character in ep.10. It's dark and violent, yet at the same time it's often light-hearted and has some really funky music. (Brynhildr in the Darkness has it beaten hands down in the darkness stakes, for instance, although I much prefer Big Order's light touch with the cliche of multiple girls fancying the hero.) Personally, though, I really went for it. I wasn't irony-watching or saying "it's so bad it's good", but instead sincerely admiring its no-holds-barred storytelling and difficult edges. I definitely need to read the manga, though.