One similarity between Much Ado About Nothing and Pride and Prejudice is that both portray love as being impossible without an absence of pride. In Much Ado About Nothing, both Beatrice and Benedick must let go of their excessive pride in order to be united. Similarly, in Pride and Prejudice, Elizabeth must rid herself of her excessive pride to be united with Darcy.
We see both Beatrice and Benedick make the decision to amend their prideful ways when they are both duped into believing that the one is in love with the other. As part of the trap, the other characters criticize both Beatrice's and Benedick's character traits, calling them both prideful and hardhearted people. We especially see Beatrice being called prideful and hardhearted in Hero's lines, "But Nature never framed a woman's heart / Of prouder stuff than that of Beatrice" (III.i.50-51). Hero also states that Beatrice is incapable of returning love (55). After hearing how badly others think of her, Beatrice decides to put an end to her pride and antagonistic feelings, proclaiming, "Contempt, farewell! and maiden pride, adieu!" (III.i.111).
Similarly, Don Pedro proclaims to Claudio and Leonato that if Beatrice proclaims her love to Benedick, then Benedick is likely to reject her and treat her with hatred because he has a prideful, hateful heart, as we see in his lines:
If she should make tender of her love, 'tis very possible he'll scorn it; for the man, as you know all hath a contemptible spirit. (II.iii.164-166).
After hearing this, just like Beatrice, Benedick decides to amend his ways, declaring, "Happy are they that hear their detractions and can put them to mending" (II.iii.208-209).
Just like Benedick and Beatrice, after Darcy is "contemptuously" rejected and "scorned" by Elizabeth and writes her a letter to explain away her negative feelings towards him, Elizabeth feels equally chastised. She too realizes that she has judged Darcy harshly as a result of her excessive pride, as we see in her lines, "How despicably have I acted ... I, who have prided myself on my discernment!" (Vol. 3, Chapter 13).
Hence, we see that the authors of both the play and the book saw pride as an impediment to true love and portrayed their characters as abandoning all excessive pride with the purpose of uniting them.