What is the major difference between the majority and dissenting opinions on false speech and the stolen valor act?

I believe the answer is: Stolen Valor had a punishment if a person lie, but in false speech the person is protected by the first amendment the freedom of speech 

The stolen valor act provide a legal punishment for people who knowingly pretend to obtain some sort of medal from millitary service in order to receive a financial or social gain . False speech on the other hand, tend to be political or ideological , and mostly still protected under the first amendment.

with my recent question