This accepted answer claims that one advantage of PoS vs PoW is that
some scalability problems can be addressed more easily with PoS
What are those scalability problems? What are the scalability benefits of PoS vs PoW?
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An obvious way to scale a distributed database is to put transaction types that will never rely on each other into two separate databases. This is such a standard practice it's difficult to find a citation for it. But if we are using a PoW blockchain to store our data we cannot do this because the smaller shard will be less secure in proportion to its size when compared to the larger chain. Let's say we split bitcoin into BA and BB. BA has 90% of the hashpower BB has 10%, that means it will take only 5.1% of the total hashpower to control BB. As it stands, no one has provided a solution to this; personally, I don't think there is one.
Since the security properties of PoS are not based on the extrinsic cost of validating the chain, the above attack is out of scope and we are free to shard/scale the network in a more traditional way.
PoS has more energy efficiency benefits, the amount of electricity needed to process the blockchain is greatly reduced. Also the probability of 51% attack will be decreased because it means having a vested stake "balance" within the network so attacking the network would not be in the users best interest since they will have to own 51% of the network to attack it. Network nodes should generally increase leading to greater distribution and a higher amount of security, nodes need to be online in order to stake blocks this is what will cause this increase and thus meaning the network is more distributed and secure. I would also argue PoS is better for ease of use since it does not need mining software or appropriate hardware.
So for Scalability, it's much easier to handle in terms of speed because it's easier to see who has what amount of the crypto than it is to see hashing power and to come to a consensus on this. There is also the aspect of that it's just plain faster. Ethereum is one of the fastest proof of work algorithms out there that is still being utilized, and even it currently gets smoked by PoS algos like Bitshares in terms of pure speed. Hence why Sharding + POS is becoming more of a need than a desire for simply being nice to the environment. In terms of block sizes and storage and state, there's really not much else to that...POW and POS are virtually the same in this aspect. So in the long run, PoS becomes much more of a necessity as the need for more transactions increases.
PoS can essentially eliminate the problem of needing the processing power and the energy to finish the PoW algorithm. As for the 51% control of a network PoS if anyone stakes the highest in the network they won't be able to control it. If they were supposed to validate a fraudulent transaction they would lose their stake as well as the ability to validate in future. It is also counterproductive for any individual to buy more of the cryptocurrency to gain more stake as the more cryptocurrency they buy the more expensive it will be. Overall PoS seems to be a better solution as it will make the blockchain safer, drastically reduce its power consumption, and reduce the time it takes to make transactions.
We had wrote about an article to explain the differences between PoS and PoW. You may refer to this link to see the full article. https://www.dapp.com/article/proof-of-stake-or-proof-of-work-whats-the-difference