The advantage is it is much, much faster as you don't need to do mining.
They do appear to have a custom set of validators, so you are trusting ripple to be honest about which validators they use.
What's the advantage over a traditional database/ledger, I mean.
I know it's faster than, say, Bitcoin, but if it's not decentralized, then the whole point of a "distributed trustless network" falls down. You're still having to trust an entity, just like with traditional banking, and their control of the currency means that they can change the rules/software down the line without external consensus.