The potential of using Large Language Models (LLMs) themselves to evaluate LLM outputs offers a promising method for assessing model performance across various contexts. Previous research indicates that LLM-as-a-judge exhibits a strong correlation with human judges in the context of general instruction following. However, for instructions that require specialized knowledge, the validity of using LLMs as judges remains uncertain. In our study, we applied a mixed-methods approach, conducting pairwise comparisons in which both subject matter experts (SMEs) and LLMs evaluated outputs from domain-specific tasks. We focused on two distinct fields: dietetics, with registered dietitian experts, and mental health, with clinical psychologist experts. Our results showed that SMEs agreed with LLM judges 68% of the time in the dietetics domain and 64% in mental health when evaluating overall preference. Additionally, the results indicated variations in SME-LLM agreement across domain-specific aspect questions. Our findings emphasize the importance of keeping human experts in the evaluation process, as LLMs alone may not provide the depth of understanding required for complex, knowledge specific tasks. We also explore the implications of LLM evaluations across different domains and discuss how these insights can inform the design of evaluation workflows that ensure better alignment between human experts and LLMs in interactive systems.