Rather than letting Norma’s persona take over his conscience, Norman instead lets her control him as Norman proper, adding another interesting alteration to the scene.
(Also, this scene was brutal as fuck, as opposed to the chocolate syrup innocence of Alfred Hitchcock’s film.)
He’s not killing Marion out of an obsession with Mother, as it was played out originally, but he’s killing Sam as a stand-in for his own lying and cheating shitbag of a dad, and having him commit the atrocity as Norman further seems to show off how shattered he is inside.
To put these scenes side by side, the comparisons and contrasts are extremely easy to point out, as the creative team wisely played it as a homage (with the specific shots of the falling shower water and the feet slipping in the blood) with some additional visual input that the film didn’t/couldn’t show, particularly Norman himself.