The big advantage over w3w is that this is open. Proprietary addressing systems are a bad thing for fairly obvious reasons.
w3w's feature where it moves an address onto a different continent because you forgot to pluralize a word is the worst idea for an address encoding.
Geocoding seems really simple until you have to build one and have customers use it.
Lots of systems have checksums. It appears to me that what3words's complexity is designed to make it intentionally difficult for someone else to reimplement.