Juliana should have kept (spoiler)
Spoilers below!!
Juliana should have kept the tape, with Thomas' claim that his parents lied about his health. Yeah, she didn't let Dixon turn it over, so Smith was still free to stop the war.
However...
That tape still had value; it could have been used to blackmail or manipulate Smith. Thomas turned himself in, so the Resistance can't try to 'flip' Smith by offering to protect Thomas... but then again, Juliana doesn't know that yet.
The tape had value.. she shouldn't have destroyed it.
Sometimes fires don't go out when you're done playin' with them.