Both algorithms underlie the modern cryptocurrency market. PoS has several obvious advantages:
increases the speed of block creation;
does not require powerful equipment;
reduces energy costs;
reduces commissions.
PoW has advantages over PoS in terms of security. It completely eliminates the possibility of a Sibyl attack (when new nodes are created that impose their policy on all other network participants). PoS can only allow such an attack if the nodes have real and huge power.
PoW also completely prevents double spending. Each new block is formed only after the completion of the previous one, while it contains information about its predecessor. Unlike proof-of-stake, forks are not profitable in the PoW algorithm, since miners are only rewarded for “true” blocks. At the same time, PoS cryptocurrencies can be attacked by creating forks. Since participants in the system do not spend "genuine" funds, they can provide support to attackers. This will lead to a longer chain, which can result in fraudsters rejecting payments.
Some types of cryptocurrencies, such as Ethereum, combine PoW and PoS algorithms. At the beginning of the network existence, proof of work is applied, and after the full emission of coins, proof of stake is introduced.
PoW is more widespread and makes it possible to receive a fair reward without having the internal coins of the system in the account. At the same time, it offers large commissions, constant competition between miners, automatic increase in the difficulty of mining coins, high energy costs and spending huge amounts of money on the purchase of equipment that quickly becomes inefficient.