What are differences and similarities between Hero and Beatrice in Shakespeare's Much Ado About Nothing ?

Hero and Beatrice are just about as opposite as night and day.
Their one similarity is that both are witty and tease each other in their own
way.

We first see Hero's modest wit portrayed in the first scene when Beatrice
makes a pun referring to Signior Benedick's fighting skills by referring to him as Signior
Mountanto and asking the messenger if has returned. Hero replies with her own subtle wit, and
like a best girlfriend who is in on a private joke and knows that Beatrice admires Signior
Benedick more than she is willing to admit, she explains to the company, "My cousin means Signior
Benedick of Padua" (I.i.30). Though the wit is subtle, we can most definitely hear the teasing
tone that Hero is aiming at her beloved cousin. We can also hear her modest, flirtatious wit when
at the masquerade, a man in a mask, whom she thinks is the prince, asks her to "walk about with
him," meaning dance with him, and she flirtatiously replies that so long as he dances gracefully,
is handsome, and says nothing she is his for the dance and her presence may even linger after the
dance has ended and she has "walked away," as we see in her
lines:

So you walk
softly and look sweetly, and say nothing, I am yours for the walk; and especially when I walk
away. (II.i.74-75)

Examples of
Beatrice's wit are far more dramatic; she especially enjoys making fun of Benedick and of
marriage in general. We see her wit being used to insult Benedick when she refers to him first as
a man with "an excellent stomach" and then as a "stuffed man," like a dummy (I.i.42, 48). We also
see one instance of her wit with respect to making fun of the act of marriage when she tells Hero
that romance is like a dance. She relates the act of courtship to a "hot and hasty dance," the
wedding to a ceremonial dance that would be performed before the state, or before the king, and
she relates the act of regretting the marriage to a dance called the "cinquepace," which is a
fast paste five step dance that goes faster and faster until the man Hero marries "sink into his
grave" (II.i.62-68).

While Hero and Beatrice have wit in common, Hero is very
gentle and submissive, while Beatrice is rebellious. We especially see Hero's submissiveness in
contrast to Beatrice's rebelliousness with respect to their views on marriage. Hero is very
submissive to her father and is willing to marry whom ever he asks her to. When Leonato
eroneously discovers that Prince Don Pedro wishes to ask Hero to marry him, Leonato encourages
Hero to accept as we see when he reminds her, "Daughter, remember what I told you. If the prince
do solicit you in that kind, you know your answer" and Hero very submissivly conscents
(II.i.57-58). In contrast, Beatrice rebells against the entire idea of marriage, as we see in her
proclamation, "[I]f he send me no husband; for the which blessing / I am at him upon my knees
every morning and evening" (23-25).