I don't know much about how WebMoney works other than what I just read on Wikipedia, but it looks like WebMoney might be best compared to a permissioned blockchain where a group of companies mine the blocks.
Proof of Stake has the advantages that anyone (with sufficient money, or by gathering into pools) can become a validator, and the system itself provides extremely strong incentives not to cheat by slashing their stakes if they do. This slashing weeds out bad actors over time, as well - once their money's gone, they can't stake anymore.
I could imagine all sorts of shenanigans that could cause a small group of companies operating a money system to cheat, either of their own accord, or forced to by a government, organized crime, hackers, etc. Much harder to attack a huge self-healing group of globally distributed validators with extremely strong incentive not to cheat.