The Hat of the People degrades slower than the Chinese commando hat, is more valuable and increases Small Guns by 5. The Perception bonus however does not carry over.
It can be found in a room in an average locked floor safe on the second floor of the Abandoned Apartments (green door, to the left if you are facing Haven) under a night table in a floor safe with average lock pick in the Uptown portion of the Pitt.
While wearing the Hat of the People, the Pip-Boy lists its effect as "combat jumpsuit Small guns +5".
It does not degrade and will always stays at 100% condition.