Paraphrases represent a human's intuitive ability to understand expressions presented in various different ways. Current paraphrase evaluations of language models primarily use binary approaches, offering limited interpretability of specific text changes. Atomic paraphrase types (APT) decompose paraphrases into different linguistic changes and offer a granular view of the flexibility in linguistic expression (e.g., a shift in syntax or vocabulary used). In this study, we assess the human preferences towards ChatGPT in generating English paraphrases with ten APTs and five prompting techniques. We introduce APTY (Atomic Paraphrase TYpes), a dataset of 500 sentence-level and word-level annotations by 15 annotators. The dataset also provides a human preference ranking of paraphrases with different types that can be used to fine-tune models with RLHF and DPO methods. Our results reveal that ChatGPT can generate simple APTs, such as additions and deletions, but struggle with complex structures (e.g., subordination changes). This study contributes to understanding which aspects of paraphrasing language models have already succeeded at understanding and what remains elusive. In addition, our curated datasets can be used to develop language models with specific linguistic capabilities.