> So it makes me wonder, is embodiment (advanced robotics) 1000x harder than LLMs from an information processing perspective?
Essentially, yes, but I would go further in saying that embodiment is harder than intelligence in and of itself.
I would argue that intelligence is a very simple and primitive mechanism compared to the evolved animal body, and the effectiveness of our own intelligence is circumstantial. We manage to dominate the world mainly by using brute force to simplify our environment and then maintaining and building systems on top of that simplified environment. If we didn't have the proper tools to selectively ablate our environment's complexity, the combinatorial explosion of factors would be too much to model and our intelligence would be of limited usefulness.
And that's what we see with LLMs: I think they model relatively faithfully what, say, separates humans from chimps, but it lacks the animal library of innate world understanding which is supposed to ground intellect and stop it from hallucinating nonsense. It's trained on human language, which is basically the shadows in Plato's cave. It's very good at tasks that operate in that shadow world, like writing emails, or programming, or writing trite stories, but most of our understanding of the world isn't encoded in language, except very very implicitly, which is not enough.
What trips us up here is that we find language-related tasks difficult, but that's likely because the ability evolved recently, not because they are intrinsically difficult (likewise, we find mental arithmetic difficult, but it not intrinsically so). As it turns out, language is simple. Programming is simple. I expect that logic and reasoning are also simple. The evolved animal primitives that actually interface with the real world, on the other hand, appear to be much more complicated (but time will tell).