Ego.

Nothing more, nothing less. Graham was so settled into the idea that the Flag, and subsequently the Overflag, and then the GN Flag was superior, that he would not settle until he had beaten a Gundam with it and then proven that it was great.

But you are right, in the end, the piece of shit GN Flag was worse than the Overflag. Graham couldn't beat Setsuna in Exia's depleted state. They "tied" and though it looks like neither pilot actually died, the entire purpose was for Graham to stroke his own ego.