Both are family themed, and a part of the plot, which is a spoiler, is kind of similar. UchiKare is a series with the combination of drama and comedy, but surely has great touching parts. It focuses more of mother and daughter relationship, and just a little bit on the side of the father. Soshite Baton is more of dramatic movie, and has also explored father and daughter relationship with the mother and daughter relationship. Bonus: Okada Kenshi is both on these ;)
The plot of the two films are very different but the atmosphere of these movies are very similar, very reminiscent of the old Japanese and Korean movies I used to watch during my teenage days. Be With You itself is a Korean adaptation of a Japanese drama, that's why I recommended the film instead the drama series. Anyway, both are family-oriented dramas with swoon-worthy teenage romance.
