There are many subtle differences between different types of POS coin. The "original" POS style, exemplified by NXT and PPCoin, involves currency holders having a pseudo-random chance at being able to create a block based on how much currency they own. This is "permissionless" like POW - there are no designated nodes. But there are many other ways to do POS - Tendermint uses a 2/3rd majority of a set validators to create new blocks. Directed Acyclic Graph (DAG) coins like Byteball and Iota use a majority of witnesses/validators to move the graph along.

POS's primary advantage is that very little energy is required to secure the network. This eventually means transactions on POS coins will be much cheaper. However, large currency holders (or permissioned validators) may be able to attack the network the way computing power can attack POW. Because these currencies are secured by signatures instead of work, it may even be possible to attack the network after "cashing out". This is called the "nothing at stake" attack, but it is much more complicated to pull off than a POW attack.

Sharding is the idea of splitting up a blockchain into multiple smaller parts so that the bandwidth required is dramatically reduced. For POW, this would require splitting POW up into multiple chains making all shards weak as the weakest shard - in theory, there may be ways to improve that security. For POS, assuming a random, uncoordinated distribution of stake/validators among each shard, attacking one shard would be as almost difficult as attacking the whole network. The probability of gaining a controlling stake over one shard would be correlated to how much total stake an attacker controls.

One thing to note about most POW coins is that they are pretty weak to attack from competitors. Bitcoin Gold was successfully attacked and an exchange lost $18m recently. Unless you have an overwhelming marketshare like Bitcoin, POW coins are quite vulnerable whereas POS are usually not.