Satsuki, her younger sister Mei and their father have just moved to their new home in the countryside, where grand adventures await them. One day while playing outside in the garden Mei encounters a small creature and decides to follow it. After chasing it through the bushes Mei eventually finds herself at the base of a large Camphor tree and as she drops through a hole in its roots, she lands on the stomach of a large, sleeping forest spirit named Totoro. The two sisters befriend the gentle spirit and are soon introduced to a world more fantastical than they could ever imagine, from playing with soot spirits to meeting a Catbus, to flying through the air and even making the trees grow. However when Mei disappears, Satsuki must call on the help of her new friends if she wants any hope of being able to find her sister...
A young girl (or two) move to a small town where the meet several magical creature-things. Unfortunately for Momo, the traditional youkai she runs into aren't anywhere near as cute as Totoro or the Cat Bus, but their intentions are just as good-hearted. Though they're extremely similar, I think Letter to Momo will appeal to an older audience than Totoro- while it's much less fun, it has more emotional nuance.
Totoro is much more light-hearted and carefree than A Letter to Momo, but they're still very similar. A small family moves into a new home, only for the children to discover that supernatural beings are living alongside them. Both are very cute and silly at times, but A Letter to Momo also touches on some emotional and difficult subjects. Still, a fan of one could probably appreciate the other.
Natsume is lonely; he has an ability that separates him from others: he can see and interact with spirits. Soon, however, Natsume discovers that he’s not alone: his grandmother Reiko also had the gift. But things get hectic and possibly dangerous for Natsume when he finds out that he also inherited the 'Book of Friends', a book that contains the names of all the spirits Reiko defeated and subjugated. He finds himself hounded by his grandmother's underlings and, with the help of a 'cat' charm spirit, decides to free them from the Book's shackles, as well as protect the book from those who seek to misuse its power...
Both of these anime focus on traditional youkai, and have matching mostly-somber atmospheres (with occasional bursts of action or comedy), a pervading sense of loss/loneliness, and washed-out color palettes. I think they'll appeal to the same audience.
If you enjoyed seeing the protagonist of one show interacting with youkai while trying to solve their problems (usually brought on by the youkai), you should check out the other. Natsume Yuujinchou includes many different adventures and stories while A Letter to Momo focuses on one, but fans of one should definitely take interest to the other. Both share a similar somber yet gentle atmosphere while the main characters also share the same experiences of loss and loneliness.
A boy arrives in purgatory after dying, where he is informed that in his past life he committed a terrible sin, and cannot be reincarnated until he can remember what it was. Until he does, he is placed in the body of a middle school student named Makoto who committed suicide three days ago, and is instructed to live the deceased boy’s life. New Makoto quickly becomes fed up with his host body's situation, as the boy doesn't have any friends, his family life is in shambles, and his mere presence makes everyone around him nervous. But giving up is not an option, and if the spirit ever wants to move on, he must adjust to Makoto's life and understand what happened in the past.
After her parents separated, eleven-year-old Miyori was left in the care of her grandparents who live in the countryside, where she lives a lonely and solemn life. While exploring the woods one day near the village, Miyori comes across a giant cherry tree and meets the spirits of the forest. They tell her that she is the guardian of the forest, a role that Miyori stubbornly does not wish to fill - that is, until she learns that a dam is being built, and it threatens to submerge her home and the home of the spirits! With the help of her new woodland friends and classmates, Miyori hatches a plan to save her new home...
While the actual storyline of the two are different, A Letter to Momo reminded me of Miyori no Mori. Both anime features a child that moves from the city to the countryside due to family reasons. While there, they both discover the ability to see spirits (or youka), and have to learn to adjust to both this ability and their new living situation.
Chihiro and her family are on their way to their new home, when they discover an abandoned amusement park. After Chihiro's family mysteriously turn into pigs, she is thrown into a surreal world of magic and fantasy. Join her as she struggles to survive in the bathhouse of the gods, ruled by an evil witch who has stolen not only her name, but her way back to the real world.
Both films are about a young girl moving to the country and having to go through difficult, 'coming of age' experiences involving supernatural beings. 'A Letter to Momo' takes a while to get going and is more 'slice of life' for the first half (the second half more than makes up for it), while 'Spirited Away' happens in the spirit world almost entirely and is a bit more exciting, with more characters. Momo's story is also very touching (and a bit more mature), because of her family situation. If you liked one, you'll most likely enjoy the other too.