I'm not a Cartesian dualist, so the difference could only be one of scale rather than of metaphysical kind. But that dichotomy seems false since differences in degree or scale can add up to ones of kind. Species and genera evolved from degrees of genetic and phenotypic differences.
So personhood evolved from primitive tendencies in apes. But once certain thresholds are reached, you have the prospect of emergent properties and of a new "natural" order.
In what sense are all the orders (planets, galaxies, mereological levels) unified, adding up to a single "universe"? In some attenuated physical or cosmological sense, sure it's all just a "natural" universe of "objects." But when new models are needed to account for what emerges, you have divergences too. You can't predict the emergence of biology, psychology, and sociology on the basis strictly of physics or of string theory. So in that sense there's no theory of everything, and thus no metaphysically unified "nature."
It's interesting to think of how species will adapt to the humanized terrain we'll have produced over thousands of years of further history (if we survive our virtual godhood or transhuman merger with technology). Certainly, other species will try to adapt, but will we let them? Will we allow any trace of wilderness (i.e. of a prehumanized state of nature) to remain?
More precisely, if we could help it with our technological power, wouldn't we prefer to humanize the entire universe? In that case, we'd permit only genetically engineered species (pets) or digital ones in cyberspace or virtual reality to thrive alongside us. That seems to me a difference in kind due to one species' conceit of having godlike power over the whole planet and over the outer wilderness too (given spaceflight).
I see this anomalousness of personhood as being foreshadowed by theistic religions, which depict the gods as ruling over the universe. The gods have always been just us, hiding in plain sight.
So are we part of nature? I'd say yes and no.