Gwen and Cecily
Like the two male leads, Gwendolen and Cecily also have a lot in common. There’s the Ernest thing: marrying a man named Ernest seems to be the founding principal of their lives. The two women even say it in unison: "Your Christian names are still an insuperable barrier. That is all!" (III.29).
Gwendolen and Cecily both keep a diary, which they believe would pretty much stand up in a court of law as proof of whatever they say. And both are willing to fight tooth and nail to get what they want... though not in front of the servants. Neither Cecily nor Gwendolen has much of a character arc, because the absurd plot simply unfolds to their advantage. In the end, Cecily does have to make do with an "Algernon." So we guess Gwendolen wins since she alone ends up marrying an "Ernest."
Why did Oscar Wilde make them so similar? Because his main interest was in satirizing the society that produced women like them—not in the individuals themselves.
Lady Bracknell Junior
"You don’t think there is any chance of Gwendolen becoming like her mother in about a hundred and fifty years, do you Algy?" (I.227), Jack asks in the first scene. Bad news, Jack. You may not be able to see beyond the blond ringlets and cute Victorian corset, but the signs are all there.
Gwendolen is opinionated and forceful like her mother; she bosses Cecily around with ease. Gwendolen also has strong ideas about social protocol, which we see in the first scene. Jack's marriage proposal has to be exactly right:
Gwendolen: Yes, Mr. Worthing, what have you got to say to me?
Jack: You know what I have got to say to you.
Gwendolen: Yes, but you don't say it.
Jack: Gwendolen, will you marry me? [Goes on his knees.]
Gwendolen: Of course I will, darling. How long you have been about it! I am afraid you have had very little experience in how to propose. (I.161-165)
The City Girl
Gwendolen has been raised in the city and is polished and sophisticated. She enjoys this advantage over Cecily, whom she considers a country bumpkin. There are a number of hilarious town vs. country barbs in their tea scene, the least veiled of which happens here:
Cecily: Do you suggest, Miss Fairfax, that I entrapped Ernest into an engagement? How dare you? This is no time for wearing the shallow mask of manners. When I see a spade I call it a spade.
Gwendolen: [Satirically.] I am glad to say that I have never seen a spade. It is obvious that our social spheres have been widely different. (II.295-29)
Based on this snippet of dialogue, it certainly looks like it's fighting time. But no—the servant Merriman enters and quickly restores calm. One woman may be a country girl and the other a city girl, but both know that you don’t let it all hang out in front of the servants.