W. Heath Robinson (an illustration of Beauty and the Beast...but most would probably assume it was Cinderella at first glance
1. The relationship of the main character to her sisters-the sisters in each tale are selfish and materialistic, mocking their younger sister. In Aschenputtel there is even a scene where the father makes a journey and asks his daughters which gifts they would like him to bring them, just like in BATB-the sisters ask for material, beautifying gifts (clothes and jewels), while Beauty asks for a rose and Cinderella asks for a branch-modest gifts of nature.
2. Both heroines must separate from a parent and transfer their affections to their lover. Anyone familiar with Beauty and the Beast will know Beauty is quite the Daddy's girl, willing to die for him, running home as soon as she finds out he is sick. Aschenputtel's only solace is the tree planted over her dead mother's grave, watered by her own tears, and the birds that inhabit it. It is the tree that provides her with gifts and enables her to attend the ball, and also the tree to which she escpes the second night after the ball.
Yet Griswold points out that, despite the "lesson" of separating from parents (which I think may have been superimposed by scholars more so than implicit in the tales themselves, especially considering this last point), in the end the heroines are able to live happily with everyone they love-Beauty's father comes to the castle, and the birds are present at Aschenputtel's wedding.
3. Love based not on appearances. This may be a stretch for some people in the Cinderella tale, because this seems to be the quintessential example of love that is based SOLELY on her being the most attractive female at the ball. However, the slipper test becomes almost like a "groom test," to see whether or not he can recognize his bride without her finery. Though he initially looks only at the feet, "eventually he turns his gaze from the shoe to her face and recognizes the woman he fell in love with."
Aw. That would be so sweet if it were true. Actually the prince appears to have no ability to recognize faces at all in the Grimm version, he is only alerted to the situation by birds telling him whether or not blood is streaming from the shoe, because the sisters had to hack off chunks of their feet in order to get the slipper on.