We compared four large language models (ChatGPT, Grok, Gemini, DeepSeek) with humans in reference to tests of cognitive development addressed to relational integration, linguistic awareness, general and domain-specific reasoning, and cognitive self-awareness. We aimed to specify how LLMs compare with humans along several cognitive development hierarchies. Given their theoretical importance for intelligence, LLMs were also asked to indicate how Descartes’s Cogito applies to them and self-rate on aspects of Artificial General Intelligence (AGI). There was a huge divide between verbal and logico-mathematical tasks, on the one hand, and visuo-spatial tasks, on the other hand. All LLMs attained perfect linguistic and metalinguistic performance. ChatGPT and Gemini matched or exceeded university-level human performance in mathematics and causal reasoning, Grok performed slightly lower, and DeepSeek weakest overall. All LLMs underperformed in visual–spatial tasks or reasoning tasks when shown visually as presented to children. Performance recovered when these tasks were presented in a fashion allowing LLMs to employ an analytical approach to visual patterns, signifying their unique architecture. Self-concept ratings broadly mirrored performance profiles: ChatGPT and Grok rated themselves high in reasoning and low in imagination, Gemini inflated imagination by reframing it as linguistic creativity, and DeepSeek consistently underrated itself. Each LLM restated Descartes’s Cogito differently as a description of itself and denied having much AGI. Hence, LLMs display human-like “subjective” task scaling implying algorithmic or functional metacognition, which captures the architectural gap between symbolic reasoning and imaginative cognition, but they are modest in claiming top human intelligence. Overall, LLMs display "savant-like intelligence" rather than top expert intelligence. Implications for an integrated natural-artificial intelligence theory are discussed. Also, a developmental engineering model is sketched that would allow removing limitations of each LLM.