In PoW, there is an unbounded cost to preventing anyone else from winning a block announcement forever. In PoS, there is a bounded cost. The shape of the curve that monsterer mentions never levels off asymptotically.
And that is why PoS can't be asymptotically permissionless, but in theory PoW can be.
That's actually quite an elegant description. It says that if I own all the stake in a POS coin, I control it forever, no one else can mine a block for the rest of its existence. In POW you can't own all the hashes in the world forever (unless you have infinite electricity) because every hash has a cost, so your monopoly is only temporary.
People will argue that owning all the stake in the world is unrealistic, but in actual fact your level of control is directly proportional to your stake, so you can start causing problems much sooner and potentially cost free if you are shorting the coin.