The Friendship Squad/Pro-Noel side is basically saying that the new world should be created without sacrificing their morals or sense of what they believe to be right. Like the Anti-Reg.
The Burn-the-Witch/Noel side wants to either eliminate the root problem by ANY means necessary to them, or fulfilling their goals even if it means making brutal decisions. Like the Pro-Reg (tho they weren't exactly aiming for deicide)
Also, wasn't Tao kinda on the Defend Noel side (in her own special way)?