The concept of Byzantine Fault Tolerance is a crucial one. It means that it is mathematically guaranteed that all parts of the Network will come to the same agreement at a certain point in time. Exactly what PARSEC achieves.
This is very different to any blockchain-based consensus mechanism. With blockchains, the probability that the consensus cannot be reversed increases with every additional block that is added to the blockchain — but crucially, it never reaches 100% certainty. Put simply, this is down to the way in which blocks are added in blockchain technology and not something that will change in the future. With PARSEC, consensus is mathematically guaranteed as certain (as well as having a throughput that dwarves blockchain tech). And this is a huge thing.
What’s more, PARSEC is highly asynchronous. This means that there is no trusted setup nor any synchronous steps involved, as might be required in common coin implementations or threshold signature schemes. In other words, any consensus mechanism has to be able to work perfectly, even when different events on the Network are reaching nodes at wildly different times and allowing for the fact that nodes may suffer technical issues around the world or the Network could be attacked.