Having read considerable chunks from Huybrechts, Voisin, Griffiths-Harris and Demailly, I want to suggest a slightly different viewpoint on the relationship between these books that hopefully complements the brilliant answer by Gunnar Þór Magnússon.
Books by Huybrechts and Demailly focus on the theoretical foundation of complex geometry, with the book by Huybrechts being considerably more elementary than the course by Demailly (the latter touches on singular complex spaces, currents and spectral sequences, to name a few). I think it would be a true statement to say that Demailly fully covers the contents of Huybrecths' book, but then provides much more on top of that. In particular, the end of Demailly's course also taps into the research interests of Demailly himself and discusses notions of positivity for vector bundles and $L^2$ estimates. The very last section of the book proves Grauert's Direct Image Theorem, which in and of itself shows how much technique is developed in the book.
Voisin's books go much deeper into Hodge theory, just as the title suggests. The beginning of Volume I covers some of the same foundations as Huybrechts and Demailly up to the discussion of the Hodge decomposition in cohomology. However, starting with chapter 7 the book goes deeper into Hodge theory proper, and culminates in the discussion of variations of Hodge structures in chapters 9 and 10. The end of Volume I lays ground for the discussion of analytic and algebraic cycles in Volume II, again something that is mentioned in Demailly on only a couple of pages. Volume II then discusses advanced topics close to the research level in variations of Hodge structures (relevant for moduli theory), algebraic cycles and fine topology of algebraic varieties. In conclusion, only about a half of Volume I overlaps with Huybrechts/Demailly.
The book by Griffiths and Harris shines (in my opinion) when it comes to examples and applications of the foundational theory. The material of chapters 0 and 1 is fully covered by Huybrechts/Demailly, and in a more detailed fashion. But chapters 2 and 4 on curves and surfaces contain a wealth of beautiful geometric material that is scattered in the literature, but here you can find it all in one place. This "examples and applications" part overlaps neither with Huybrecths/Demailly nor with Voisin.
PS. I am not really sure whether there exists a better exposition for parts of chapters 3 and 5 of Griffiths-Harris. In case there does not, it should still be considered a go-to resource to learn about applications of currents and residues in complex geometry.