About HArtshorne and Griffith, I think a comparison between the two texts is misleading.
The first is a introduction to the "Grothendieck ioga" where geometrical classical idea are "immersed" in the more large but abstract mathematical world of schemas.
But also if the Complex differential manifold style of Griffith is "more concrete" is very different from the "Algebraic Geometry" idea, also if it is a deep study of it.
As categorist I love Grothendiek, but I find Grothendieck work fantastic in itself (like a music), also if I never understand nothing about Geometry Geometry while studing or readind EGA or some SGA.
FOr understant what is "ALgebraic Geometry" I had to read this
Beltrametti-Carletti-Gallarati-Monti Bragadin, Letture su curve, superficie e varietà proiettive speciali, Boringhieri
Beltrametti-Carletti-Gallarati-Monti Bragadin, Lezioni di geometria analitica e proiettiva, Boringhieri
(sorry, these are in Italian)