circumstances, we have video evidence that he clearly meant to punch her in the face. Whether he meant to punch her "as hard as he could" or only "hard enough to teach her a lesson" is irrelevant in this case. Either scenario is sufficient to provoke outrage. Moreover, it is clearly not appropriate for him to "discipline" his fiancee in anything that resembles how that scenario played out.
Adrian Peterson clearly disciplined his child too strongly (he admitted as much), however, it is not clear that he intended to cause that degree of harm. Whether he spanked/whipped him "as hard as he could" or only "hard enough to teach him a lesson" is VERY relevant in this case. One is clearly a crime, the other is a very sad and unfortunate mistake. Our opinions may differ on what how we think it played out, but there is a very real possibility he did not intend to injure the child. There is plenty of room for reasonable people to withhold final judgement in this case.
We should therefore not be surprised (reference to your original post) that there is a difference in the level of public "outcry".