So the question of this thread is:
Which is superior - objective morality or subjective morality
My answer is "Whichever one of them is correct". And since I can't support that either are correct and as far I know, no one else can either, the answer to that question is "I don't know" and likewise the position of this OP is that we don't know which is superior.
So to defeat the OP, one has to show that either
1. One of them is correct and the other is incorrect
2. One of them is superior even if it is incorrect and the other is correct (which isn't impossible as sometimes a lie is better than the truth such as telling your child an untruth to dissuade him from doing something dangerous).
I'll quickly define terms (although one is free to offer better definitions although I don't want to get bogged down in debating this).
There is an external moral source that forwards objectively correct morals that people are always correct if they follow. For example, God says Murder is wrong and therefore to disagree with this moral position is to be objectively wrong in the same vein as saying that the earth is flat.
Morality is a human invention and whatever is wrong is whatever a person happens to think is wrong and it is determined person to person (but then certainly moral issues, such as murder and rape, seem to be forwarded as consistently wrong by a vast majority of people).
And again, I argue that whichever is correct is the one that is superior. If objective morality is correct, its superiority to subjective morality is obvious so I won't spell it out. In the case of subjective morality, if it is indeed true that morality is a human construct, I see no reason why failing to acknowledge this reality and acting on the truth would not be superior to falsely believing that there is an objective source of morality. Again, while a lie can sometimes be preferable to the truth, I don't see this situation as an exception.
So again, since we don't know which is true and which is false, we also don't know which is superior to the other.