Humans organize knowledge into compact categories through semantic compression by mapping diverse instances to abstract representations while preserving meaning (e.g., robin and blue jay are both birds; most birds can fly). These concepts reflect a trade-off between expressive fidelity and representational simplicity. Large Language Models (LLMs) demonstrate remarkable linguistic abilities, yet whether their internal representations strike a human-like trade-off between compression and semantic fidelity is unclear. We introduce a novel information-theoretic framework, drawing from Rate-Distortion Theory and the Information Bottleneck principle, to quantitatively compare these strategies. Analyzing token embeddings from a diverse suite of LLMs against seminal human categorization benchmarks, we uncover key divergences. While LLMs form broad conceptual categories that align with human judgment, they struggle to capture the fine-grained semantic distinctions crucial for human understanding. More fundamentally, LLMs demonstrate a strong bias towards aggressive statistical compression, whereas human conceptual systems appear to prioritize adaptive nuance and contextual richness, even if this results in lower compressional efficiency by our measures. These findings illuminate critical differences between current AI and human cognitive architectures, guiding pathways toward LLMs with more human-aligned conceptual representations.