Not an NLP expert but the biggest difference in my experience is guided focus, so to speak. When summarizing something huge like the US Code, for example, you can tell the LLM to focus on specific topics and anything adjacent to them so that it ignores irrelevant details (which is usually >99.9% of the text in my use case). The word relationships encoded in the LLM are really good at identifying important adjacent topics and entities.

LLMs are also really good at the harder NLP problems like coreference resolution, dependency parsing, and relations which makes a huge difference when using recursive summarization on complex documents where something like "the Commisioner" might be defined at the beginning and used throughout a 100,000 token document. When instructed, the LLM can track the definitions in memory itself and even modify it live by calling OpenAI functions.