I don't see the difference, unless we are going to say Memory is weaker at affecting memories than Authority, it should be able to do many of the same things defensively, make them forget they wanted to attack you. Implant memories of intense pain, or destroy someone's memories in combat, make them forget to attack, make them forget who they are, until they are a shell.
I'm not talking about affecting Memories, I'm talking about overall effectiveness. Authority doesn't need to affect Memories to be better than Memory.
Outside of combat, the only true edge Memory has over Authority is personal knowledge accumulation, which isn't that important. While an Authority user could just have anyone (who isn't powerful and resisting) do anything, a Memory user could only collect the information they want. They'd need to act on it themselves.
For comparison, let's say an Authority user and a Memory user both want to create some superweapon. The Authority user could just control the world's greatest minds to do it themselves, as well as control others to get resources and the like. A memory user, meanwhile, would struggle to find those same people (Authority could easily do that via access to government), and even when they manage that, they'd need to work on everything themselves, which would take much, much longer.
If we stretch it, they might be able to slowly reconstruct a person's memories to create a similar effect to Authority, but that is a very roundabout way that couldn't be mass-produced, or at least, not on the level of Authority.
In combat, it wouldn't be nearly as effective either. Memory might be able to make an enemy forget they want to attack, or stun them via certain memories, but the enemy's attack would still be moving. Authority could make the enemy stop attacking. Or bite their tongue. Or attack themselves. All the while, their countless slaves are firing at you with superweapons their other slaves made. And even if you escape, you're already an outlaw, because they control the government.
Also, I am almost sure you can't cause permanent harm to someone's memories with power relative to yours that easily. Just like an Authority user can't just completely control someone who is relative to them and resisting, and like how a resisting superhuman could undo shapeshifting caused by someone relative to them in power, Memory should have the same limitation. Any "permanent" damage is only permanent until the effect is broken.
What makes Authority stronger than Memory (or our current understanding of it, at least) is what it could do in the limited amount of time it has to act. The enemy forgetting how to attack for a second, hell, even a minute, doesn't matter if nothing you do can harm them. But the enemy attacking themselves?
Much more viable.