Canonically, Chaotic Good will always be the "greater good" and Lawful Good the "just and goodly". If you are playing the straight and narrow or closer to Exalted type rules, there's no option but to really abide by the "classic" staple of honor. If you are going by the newer interpretations, "honor" need not be societal honor anymore; you need honor only your code and your beliefs, of which are inherently good because of their tenants and their source. This results in some more unusual and newer interaction, in that Lawful Good might just be outright opposed in beliefs to Lawful Neutral societies.

I think this is in part why you see the Oath of the Crown in addition to the Oath of the Devotion in the current edition.