Peter did the exact same thing as Walter
It seems like one of Peter’s goals in Fringe is to “Be a better man than his father”, but when faced with a problem he reacted in a nearly identical way.
When Walter lost Peter he became obsessed with getting his son back, even going to another universe to retrieve him, but it destroyed his relationship with those around him, including his wife who ended up committing suicide because of his actions.
Then there’s Peter, whose daughter is taken by observers. He becomes obsessed with finding her, unable to move on with his life. His obsession and unwillingness to accept reality causes him to loose Olivia.
Peter isn’t a better man than his father.
He is the same man as his father.