Both films tackle the same thing: the struggle of a single man taking care of a child he barely knows. Usagi Drop is a little bit in the dramatic side while Baby and I is a little bit in the funny side, in my opinion. And the little difference is that the child in Usagi Drop is six years old while in Baby and I, the child is still an infant.
These films are soooooo funny. You'll watch them and laugh so hard. what happen to both the protagonists are hilarious and they have serious melt-downs. If you seriously need to have good laugh and you also liked Fasten your seatbelt than watch Baby & I. They're both fantastic. Such a LOL. though be prepared for profanity.
These movies are similar because both have young men some how becoming the caretakers of a baby. The male-leads both struggle with their new found responsibilities as a father and also have romantic side-plots. Overall they both have a similar feel with the comedic elements and feel-good family vibe they share.