This is a classic beginning to many Victorian novels: take two girls (check), usually a brunette and a blonde (check), whose personalities are markedly different (check). Then turn them loose to see how well they do. Since they are girls, and since this is Victorian times, that usually means "how well they marry."
Young women are expected to just let life happen to them, rather than grabbing the bull by the horns. For Becky, this is a double bind, as Thackeray points out. On the one hand, Becky doesn't have anyone behind her to orchestrate a marriage, so she has to actively pursue her own options (Jos, for instance). On the other hand, being too aggressive opens her up to being called un-feminine and being seen as a sleazy gold-digger. Amelia is also in a double-bind. On the one hand, what makes her so likeable (we are told) is how soft and undemanding she is and how much she is willing to just accept whatever life gives her. On the other hand, this kind of femininity also makes her super-boring and taken for granted.
The stories of the two girls sync up nicely, with some good contrasts. Both have made financially dumb marriages. But Becky is the loved one in her marriage, while Amelia is the one who is doing the loving. Becky is still scheming and plotting and trying to move forward in the world, while Amelia sits patiently at home waiting for George to come to his senses and start to appreciate her.
Again the two women's stories sync up somewhat, even though the paths they took to get to their lowest points are as different as can be. Still, at the climax of the novel, both Becky and Amelia have lost everything of value. Becky's respectability, high social status, and a chance at great financial success are gone. Gone too are Amelia's two loves, her comfortable lifestyle, and her self-respect and dignity.
Becky is inexhaustible and never gives up. She is the novel's eternal optimist, especially about herself. As soon as Rawdon leaves her, she immediately sets off to get his brother Pitt to reconcile them. When that doesn't work, she bums around Europe until she runs into a still-furious Lord Steyne, and without skipping a beat she tries to see if he'll have her back. Amelia, meanwhile, sinks back down into mopey mode, sighing over her dead husband and ignoring the long-suffering Dobbin. She doesn't even have the mental energy to get past a two-month marriage that ended ten years earlier.
Again, a bit of a matchup here between Becky and Amelia. Both end up settling for a second-rate marriage (well, couple-ship, since Becky and Jos cannot actually get married). But still, both at last find what they had wanted from the very beginning. In Jos, Becky has financial security for life. In Dobbin, Amelia has a husband who will baby her and allow her to lead the kind of passive, boring existence she prefers.
It's a mega-happy ending for all! Just kidding. Thackeray never lets the cat out of the bag, so we readers get to decide for ourselves. What do you think happened to Jos? Will Dobbin and Amelia still be relatively content in middle age?