If "Where's the beef?" is asking for substance relating to an issue, "What's your beef?" is asking what substantive issue to have with someone or something.
Related: "Having a beef" with someone or something.
Example: "I don't like that Barbara." "What's your beef with her?" "Nothing - I just don't like her attitude."
In this case, the speaker has not had a personal conflict with Barbara of any substance. It is not that Barbara stole money from the speaker, damaged the speaker's car, or threw a rock into a window at the speaker's house. The annoyance with Barbara is strictly based on superficial issues.
If Barbara had done some tangible wrong to the speaker, this would be the speaker's "beef" with Barbara.