Compare the Little Red from the traditional tales with Carter's rendition of the character. How does she empower this character in her story? What knowledge and experience does she acquire in Carter's story?

Angela Carter is known for her darkly feminist reinterpretations of classic fairy tales. "The Company of Wolves," her re-imagined Little Red Riding Hood, is no exception, and gives us an empowered young protagonist who takes charge of her own story.
Little Red Riding Hood is a tale that has been reinterpreted and translated into many languages and cultures. Two of the most famous versions of the story are Charles Perrault's 1697 version in the French "Le Petit Chaperon Rouge" and the Grimm Brothers 1812 version in the German, "Rothkäppchen." In both of those versions, Little Red is minimally but effectively characterized as young and sweet. Perrault says she was "the prettiest creature who was ever seen" and the Grimm Brothers say "everyone who saw her liked her." Her characterization doesn't go much further than that, but that is the traditional way of fairy and folk tales—characters are often "flat" (uncomplicated personalities, unchanging over the course of the story) in order to best display a sense of universality / archetype, since the stories were often moral tales. In fact, Perrault's version ends with a moral:

Moral: Children, especially well bred, attractive young ladies, should never talk to strangers, for if they do so, they may well provide dinner for a wolf. I say "wolf," but there are various kinds of wolves. There are also those who are charming, quiet, polite, unassuming, complacent, and sweet, who pursue young women at home and in the streets. And unfortunately, it is these gentle wolves who are the most dangerous ones of all.

Carter's short story, however, turns the original on its head, not only through its dark ending which refutes the above moral absolutely, but also through Carter's complex characterization of her Little Red character. As with many of her feminist retellings, Carter gives the young protagonist agency in her own story and lets her go to places (morally, physically) which we have been taught not to let little girls go. Carter introduces her protagonist as a "strong-minded child" who is perhaps not as savvy as she should be. In a country where "children do not stay young for long" but "work hard and grow wise," the girl was indulged as the youngest child by her mother and grandmother. She heads off into the woods, and "she has her knife and she is afraid of nothing." So when she encounters a man whom she guesses is a hunter in the woods, she is not wary of him at all. When he strikes a deal to see who can reach her grandmother's first, she knows not to leave the path, doesn't believe in his shiny compass that he says will get him there quicker, and only blushes when he says his prize is a kiss.
We see a striking complexity in her character when the two meet again in her grandmother's house. The girl can sense something is wrong when her grandmother isn't there, and when the hunter blocks the way out, she wishes in that moment that she had her knife. There is her fear, finally. But almost immediately after, when a pack of wolves gathers around the house, howling in the snow, she remarks, "It is very cold, poor things... no wonder they howl so." Fear and empathy in the same moment—that is not a flat character in any way. Then finally "since her fear did her no good, she ceased to be afraid" and she strips for the wolf and kisses him, and when the classic line appears "All the better to eat you with," she "laughed at him full in the face" because "she knew she was nobody's meat." This self-possession and agency, even in the face of probable death, allows the girl to take the wolf to bed, eat the lice from his pelt, and sleep "sweet and sound" between his paws. Is she direly foolish? Is she the real alpha wolf? Or is she really dead? The ending is open enough to interpret a variety of ways, but the self-confidence and brash courage she displays are clear across them all.
http://www.pitt.edu/~dash/perrault02.html

https://www.pitt.edu/~dash/grimm026.html