Large Language Models (LLMs) demonstrate remarkable linguistic abilities, yet their capacity to construct coherent internal representations of discourse remains an open question. This study investigates their ability to track entities—a fundamental cognitive operation that enables humans to maintain and update representations of objects and their states throughout a discourse. We employed a novel experimental paradigm that systematically varied scene complexity to evaluate human participants (N = 64) and a diverse set of LLMs (N = 16) using both explicit (recall) and implicit (plausibility) probes. Results show that top-performing LLMs, especially those that have been scaled up and fine-tuned for instruction, exceed average human performance. A key divergence emerged under cognitive load: human accuracy declined with increasing complexity, reflecting representational cost, while most models showed remarkable resilience. However, performance was not uniform. Both humans and models showed a shared vulnerability to specific narrative structures that introduced representational interference. These findings suggest that while LLMs have acquired an important semantic competence, their underlying operational mechanisms are fundamentally different from those of human cognition. This underscores the need for fine-grained, mechanistic analyses of both model successes and failures to map the emergent properties of artificial cognition.