There are both similarities and differences in the father-daughter relationships found in both Jane Austen's Emma and Pride and Prejudice. Since in Pride and Prejudice Elizabeth is her father's known favorite, to simplify things, we'll focus on Elizabeth for our comparison of Pride and Prejudice.
One similarity between both Emma and Elizabeth is that both have a degree of control or influence over their fathers. Emma especially has greater influence. In fact, the book Emma opens with a description of Emma that points to her father being overly indulgent and that Emma actually had complete control over the household:
She was the youngest of the two daughters of a most affectionate, indulgent father, and had, in consequence of her sister's marriage, been mistress of his house from a very early period. (p. 1)
We particularly see her control and influence over her father when she guides him in their conversations. In fact, it can even be said that the role of parent and child has been reversed; Emma parentally guides her father, who acts like a child afraid of going out into the world and needing instruction. An example of the reversed child-parent relationship can also be seen in the very first chapter when Mr. Woodhouse complains of going out to visit Emma's newly married ex-governess at Randalls, saying silly things Emma must address, such as how it is too far for him to walk and too short a distance to merit using the carriage, and what will the horses do while they wait at Randalls? Like a parent educating a child, Emma explains that of course they would take the carriage and the horses would be put in Mr. Weston's stable while she and her father visited him and the new Mrs. Weston.
Similarly, Elizabeth also saw her father as needing instruction, but the difference lies in the fact that Mr. Bennet was far too stubborn and prideful a man to admit his errors until it was much too late. What's more, he too was guilty of overly indulging his daughters, especially his youngest, which were the silliest, simply to get them out of his hair. One example of Mr. Bennet needing and Elizabeth attempting to give him instruction can be seen the moment Lydia is invited to Brighton with the regiment as Mrs. Forster's "particular friend." When Elizabeth hears Mr. Bennet has given in and consented to Lydia going to Brighton with the rest of the officers, she attempts to warn him that if he, as their father, continues to let Lydia carry on with her reckless flirtations, than Lydia "will, at sixteen, be the most determined flirt that ever made herself and her family ridiculous" (Vol. 2, Ch. 18). In return, her father refuses to listen, arguing only that Elizabeth and Jane will always be respectable, no matter what Lydia does. In consequence, as Mr. Bennet soon learns, Lydia runs off unmarried with Wickham, threatening to endanger the reputation of the whole Bennet family.
Hence, there are similarities with respect to how both Emma and Elizabeth feel the need to treat their fathers but differences with respect to how their fathers react in turn.