In what you outline above, regarding the two readings and the various translations, there are, it seems to me, three views being taken.
- That God is expressing something from within himself towards all men.
[Nominative] "Good will toward men."
- That God is responding to something good that is in a certain class of men.
[Genitive A] "men of good will"
- That God is actively favouring a certain class of men, irrespective of their own disposition.
[Genitive B] "men of God's good pleasure"
The first situation requires repentance from individuals within mankind, first, before they, then, believe unto justification.
The second are already righteous because of what is within them.
The third already have God's pleasure because he has decided, arbitrarily, to favour them.
With regard to the question 'Why would one of the two genitive preferences be preferred ?' I can only assume it would be as a result of personal religious experience.
Personally, I found it necessary to repent, and then I believed unto justification, so my personal experience falls into the first, nominative, category.