Genco is only referred to in GF-1 although in cut scenes he is visited by the family while he is dying. I can understand why this was cut -- there would be later scenes in a hospital with Michael and those scenes are central to the movie. But I believe Sonny mentions that Genco was consigliere when he berates Tom.
It is in GF-2 that we see this same Genco (although that might not be clear) excitedly want to introduce Vito to his girlfriend but then slink out when Fanucci holds a knife to her throat, even though Vito seems to signal that he will help Genco fight (indeed kill probably in that situation) Fanucci but Genco is plainly afraid.
So does it make sense that Vito would make such a cowardly person (there is no other way to describe him) consigliere and he apparently, despite his show of cowardice so many years before, is a very effective war-time consigliere which Sonny feels Tom is not? I don't recall if in the book the theatre scene is present and if it is present, whether an explanation of how Genco became consigliere despite this is provided.