What Are the Differences in Security Vulnerability between PoW and Proof-of-Stake (PoS) Consensus Mechanisms?

PoW security relies on the economic cost of computational power (hash rate), making a 51% attack a massive capital expenditure. PoS security relies on the economic cost of acquiring and staking 51% of the total coin supply.

A PoS attack is generally cheaper to launch but carries a higher economic penalty: the protocol can "slash" the attacker's staked coins. PoS networks also face a "nothing at stake" problem, which PoW does not.