Goodell, based on what a lot of talking heads are saying, is sending a strong message primarily because he was viewed as vastly under-acting in the Ray Rice case. It seems a bit draconian to a lot, but I agree with Goodell's 3 major points: a. Peterson is a lot bigger; b. Peterson used the tree branch on the child on several occasions (I believe he plead guility to the assault); and c. Peterson saw nothing wrong in 'whooping' his child in such manner.
Peterson will appeal the year long suspension and will likely get some reprieve. Goodell will take any lumps from the appeal's decision considering it a PR and statement 'win' that he viewed Peterson's actions in the strongest manner possible. Ray Rice's actions deserved much more than an initial 2 game suspension. Peterson is likely paying, in some ways, for Rice's actions and Goodells inactions.
Hopefully these incidents will lead to a cultural change; the NFL has a PR commercial right now with a lot of the star players in it making comments that such behaviors are always wrong. It's about time.