I have simplified the wording of your question. Comparing and contrasting characters and their relationships is a common essay assignment. So that you might, with some suggestion from me, create your own comparisons between these couples, I have pasted a link at the bottom of this answer to the Enotes page on this topic. You'll find the suggestions given here for creating a "Comparison/Contrast Essay" very helpful.
All character (and character relationship) analysis is subjective, which means that it is based upon a personal opinion that is supported with evidence of specific examples from the text. I'll provide some suggestions for you of ways that these two couples are similar and different, then you can create your own comparison. Be sure to support your observations with examples from the text.
Hero and Claudio:
- Don't know each other well at the opening of the play.
- Are openly in love (infatuated?) with each other from the beginning of the play;
- undergo a huge test to the strength and potential longevity of their love when Claudio accuses and rejects Hero;
- Spend very little of their onstage time in conversation together;
- Proceed from engagement to marriage in very conventional ways that include Hero's father Leonato;
- Are reconciled (despite the hardship of the middle section of the play) for marriage and a happy ending.
Beatrice and Benedick:
- Have already known each other for a long time when the play opens;
- Are determined not to be in love (with anyone), even though all the other characters see their affection for each other;
- Spend alot of their onstage time together in witty and contentious conversations;
- Are conventional in their course of engagement, as Benedick asks Leonato for Beatrice's hand;
- Have their love strengthed by adversity, rather than weakened;
- End the play, much to their own chagrin, prepared for marriage and a life of love.
Shakespeare commonly presented love relationships that contrasted greatly with each other in his comedies. He would often present a young, somewhat naive conventional couple in contrast to a more witty, worldly and wise couple as he does here. The Taming of the Shrew is an example of a play with similar pairs of lovers.
For more on writing a Comparison/Contrast essay and on the couples in Much Ado, please follow the links below.