Chocchan Monogatari

Both movies are the point of view of a mother (Chocchan/ Cho Kuroyanagi) and her daughter (Totto-chan/ Tetsuko Kuroyanagi). The time period represented are different as Totto-chan's centers around her school life from ~1941 to ~1944 and Chocchan's starts when she meets her husband in 193~. Both of these movies are adapted from Tetsuko Kuroyanagi's biography and Cho Kuroyanagi's autobiography. 

Chocchan Monogatari is like the spiritual predecessor to Kono Sekai no Katasumi ni, with both dealing with Japanese families trying to live a normal life whilst World War II was ongoing. Both also have a likable cast and can be very sad. (Also, Chocchan is a great hidden gem that is pretty hard to find but well worth your time) 

Both movies tell a tale of civilian suffering during WW II, but Grave's story is much more sadder. Chocchan could be described as "Grave of the Fireflies lite".