The Cranes Are Flying is often lumped in with Ballad of a Soldier - both films came out of the USSR in the late 50s, the years after Stalin's death when cinema was finally able to thrive, and both films focus on World War II, where the country lost by many estimates 10 million people - a truly staggering number - but eventually emerged victorious. Indeed, the two films sit just two spine numbers away from each other in the Criterion catalog (the modern masterpiece In the Mood for Love sits between them), indicating that they were clearly planned in tandem.
While all of the similarities (particularly the USSR origin) make the grouping understandable, it's hard to imagine two films that are technically more different than these two. While Ballad of a Soldier is elemental, poetic cinema, The Cranes Are Flying is flashy, abstract, and contemporary. The movie's greatest moments are big loud sequences, beginning with the angular framing of the opening scene that establishes the film's cinematic language and peaking with the undercranked sequence in which Veronica, the film's protagonist, rushes after a train.
The key phrase in that sentence might be "cinematic language," as this zeroes in on what makes these two Russian films genuinely linked in film history. Because the USSR was really just beginning its move into modern cinema, both films were first stabs at an answer to what was being produced in the US. Each movie could easily have defined Soviet cinema post-WWII - they are that elemental and moving. While The Cranes Are Flying is the easier pick, I actually preferred Ballad of a Soldier, mostly because I think it is more difficult to make a film in such a simple way, and the rarity of success makes it more exciting. I also felt like many of the techniques and even the moments of true exploration of the Soviet experience (e.g. the father dismissing the propaganda line) hid a mostly conventional plot with a clear villain and a standard heroine. But a preference for this earlier film is totally understandable, and really the most obvious thing that both films share is that each one is a masterpiece that has lasted and will last long beyond its country of origin.