I will focus more on what I found to be bad about the manga. This is because many find it to be great. Therefore I felt like pointing out the bad, would have more usefulness, as many before pointed out what they found to be good.
*Big spoilers ahead, proceed with caution.*
This manga is described as horror, and in other places but not here as psychological thriller. The anime is described as psychological thriller, and I quite honestly would more describe it as such, and not horror. Only the first season of anime, and corresponding manga chapters can be described as such.
That being said up to their escape Promised Neverland is great. It really does deliver what it promises. You do feel a sense of tension. You are scared because you don't know if the children will die because of shipment, die due to being caught, or just die in the process of running away. Isabella is a great character. She is the entirety of the psychological thriller in those chapters, and does it oh so well. Her facial expressions, fake smiles, and in the end showing her true nature are really indeed scary. I still like sister Krone, and found her death scene, as morbid as it sounds. One of the best parts of the anime. I still find the portrayal of her character as racist. Call me sjw police all you want, but you cannot deny the fact, that her features get bigger when she is to be scary. This is only a small portion of the manga, so it doesn't save it. So what happens after that? Well they decided to put some nice plot armour on the children. They can't get too cold can they? The hole horror/psychological thriller aspect dies, when the children cannot. The fact that Norman survives, also takes away from the impact of first chapters. You might say well other characters die, but I never felt while reading it that they mattered. Only Yuugo's and Lukas's deaths, and Krone's I guess. Does it matter when you know that no matter what happens main characters will stay untouched? Emma cuts of her ear? No impact on plot, and gets immediate help when fainting. They almost get caught and Emma faints? Immediate rescue. Emma gets injured in Goldy Ponds and needs immediate help? No problem, no further effects on her health or anything. Here I have to say that the Goldy Ponds or w.e its called was good, I enjoyed it. Their base blows up? Immediately found by Norman's group. Someone needs medication? Let's break into a plantation and get it. Here I will stop to point out how easy destroying plantation/raiding it is shown to be. In this particular moment they are just running around, while Emma and the other one gets the meds. Just running around is enough for the demons to not be able to do absolutely anything. Have to kill the entirety of the royal family? No problem for them. The story also poops on Normans death, and its importance to the plot. Norman should've ended up being Adam, if they wanted him to stay alive. Norman just is alive, and yeah it was suggested he went through hell in Lambda. In my opinion it wasn't shown enough, meaning it doesn't have any impact on the reader. AND ALSO he just goes out of there seemingly unscathed. They don't actually show any psychological trauma. They do say "oh he had disease", and show spasms of someone else. Just to say 'SEE? SEE? THEY SUFFER!". When in reality it's not much shown how much it's affecting them or how bad it is. ON TOP OF THAT they find a cure to it. Can't remember how long it took them from mentioning to finding cure. All I can say it felt pretty damn fast to me. Again ScArY spasm disease? No impact on anything ever. The queen has two cores? Don't worry she immediately dies herself. Musica and Sonju Captured and about to be executed? Don't worry some bad guy from goldy ponds had a change of heart! I really could write out more instanced, but its getting long. I liked how they explained why the demons would even step away from eating human meat. I found that to be a decent explanation. Grandma being killed instead of Isabella is a joke. Just another way of giving a children a way to make it to their goal. Another joke of a scene is when the queen is about to die or dead, and all of the faces of characters who died are shown and they say "my name is...". Why? They were eaten? How? Whats the purpose? It only looked dumb. Another joke is that Emma just without any thought process, or emotional turmoil goes into "no genocide". I get why she took that approach, but we didn't see her getting there. It would be interesting to see. Considering what she went through with the demons. Yeah she be like that, but still. "No genocide" should not be such an easy approach to her, they should've shown her something to cause that. The price she has to pay for the promise? Fanservice. She doesn't pay a price, they find her anyway. The entire point of this review is to say Promised Neverland is not horror nor psychological thriller. Calling it that is offensive to those genres. Considering they gave their characters plot armour, and build the entirety of the world to fit their goal. Example the way demons work. There was no way they would not succeed. By doing so they very effectively stripped away all that could make it those genres.