Modern affective computing systems rely heavily on datasets with human-annotated emotion labels, for training and evaluation. However, human annotations are expensive to obtain, sensitive to study design, and difficult to quality control, because of the subjective nature of emotions. Meanwhile, Large Language Models (LLMs) have shown remarkable performance on many Natural Language Understanding tasks, emerging as a promising tool for text annotation. In this work, we analyze the complexities of emotion annotation in the context of LLMs, focusing on GPT-4 as a leading model. In our experiments, GPT-4 achieves high ratings in a human evaluation study, painting a more positive picture than previous work, in which human labels served as the only ground truth. On the other hand, we observe differences between human and GPT-4 emotion perception, underscoring the importance of human input in annotation studies. To harness GPT-4's strength while preserving human perspective, we explore two ways of integrating GPT-4 into emotion annotation pipelines, showing its potential to flag low-quality labels, reduce the workload of human annotators, and improve downstream model learning performance and efficiency. Together, our findings highlight opportunities for new emotion labeling practices and suggest the use of LLMs as a promising tool to aid human annotation.