Aishiteruze Baby★★, Fruits Basket Recommendations
Although there's really no similarities [storywise] between the two shows (other than they're both technically slice of life comedy dramas), they both have the same look and feel to them. They're both heartwarming, and have a great deal of development in both the main and side characters.
If you liked Aishiteruze Baby then you'll like Fruits Basket.
In both series, the characteristics of the main characters are similar. There is also a sweet atmosphere of the series that makes you want to watch more and more. It is also innocent and portrays realism despite the fantasy genre in Fruits Basket.
In addition, there is comedy, drama, and later romance in both series. Heartwarming tales.