The Republic becomes the Empire. The Empire does not become the New Republic, it becomes the First Order.

The Rebels form the New Republic, and later the Resistance.

It would be very strange if these teams swapped uniforms, so to speak.

The First Order’s stuff is new and spiffy because so are they. That doesn’t make them in charge, and they’re not. The Resistance is scrappy because they aren’t in charge either, they’re a separate group created by members of the New Republic. As to whether or not they should have armor is a legitimate question but in my mind it would make no sense whatsoever for them to look like stormtroopers.