As a Frenchman I'd say that both are equivalent. I would not deduce a meaningful difference in hearing the former or the latter.
From a grammatical point of view, in the first sentence I would see "le nez plongé dans mes livres" as an adjective phrase, while in the second one, "le nez" is complement the "avoir" verb and the rest describes "le nez". Hence, we might say that the first one refers more to a general state description, and maybe even a metaphorical one, while the second one actually focuses on this nose and where it is, so is more literal.
But again, this is if I really try to find a difference at all costs.