The main security difference is that with PoW any attempt to create a fork has a cost. With PoS, slashing can be used to impose a similar cost. But that doesn't work for very that long forks (longer than it takes for stakers to unbond), since the accounts being slashed might no longer exist on the main fork.

In order for validators to distinguish the main fork from any malicious long forks, they must start with a trusted checkpoint that's less than X days old, then sync at least every X days, where X is the unbonding period.

The "trusted checkpoint" notion seems to cause a lot of concern, but in my mind it's relatively harmless to just bake checkpoints into the client code (if done carefully - https://news.ycombinator.com/item?id=29370309). Most clients already have some form of trusted checkpoints (even Bitcoin Core does, though they're deprecated), or at least a genesis block, which is effectively a checkpoint.

More here: https://eth.wiki/en/concepts/proof-of-stake-faqs#what-is-wea...

And some good discussion here: https://twitter.com/zooko/status/1045807027992182785