Here are a couple of things I find are compelling security arguments for proof-of-stake.
Proof-of-work security is proportional to cost of work
With proof-of-work, security is proportional to the real world costs of the actual work. This is the real world costs of electricity, equipment depreciation, rent, taxes etc. that go in to produce “the work”.
Proof-of-stake security is proportional to value of capital
With proof-of-stake, security is proportional to the value of the staked capital (Ada). But, the cost of this capital is only around 3-5% of its value at current interest rates. (Any other real world costs in running the computers are minimal by comparison.)
In other words, the security of Cardano’s proof-of-stake system costs around 20-30 times less than a proof-of-work system with the same level of security. Or, put another way, the security of Cardano’s proof-of-stake system is around 20-30 times greater than for a proof-of-work system with the same costs.
The other thing I find compelling is the different effect of the “skin in the game”.
Proof-of-work “skin in the game” has alternative uses
The skin in the game for proof-of-work is the computing power. This is a real world resource with alternative uses.
Proof-of-stake “skin in the game” does not have alternative uses
The skin in the game for proof-of-stake is the token (Ada). This token does not have alternative uses outside of Cardano.
The important corollary is that using computing power to attack a proof-of-work system does not devalue that computing power. You could even short Bitcoin and profit on the downside. For example, someone could re-purpose government super computers + some mining rigs for a few days to obtain 51% of Bitcoin’s hashing power to do some double spending. Later you can hand this computing power back and it can be put to work doing something else. You haven’t destroyed its value because it has alternative uses.
On the other hand, if you acquire 51% of the Ada supply, and then use this to attack Cardano, then you have now devalued your own asset. Furthermore, you would not be able to adequately hedge your downside loss for 51% of the supply. If you held 51% of the Ada, you would be attacking your own asset and you are unable to re-purpose this asset.
These reasons, plus some others, is why I believe proof-of-work is a dead end.