I am not very familiar with the Polkadot tech, but in terms of the tech, I think its very similar. The Peerplays and Hive blockchains will run side by side and assets can flow back and forth. (For now only HIVE and HBD). Similar to the parachain paradigm, the flow of assets, ie the value transfer via an elected, decentralized set of nodes called as SONs.

The following diagram will help to understand the asset (value) flow between chains.

https://devs.peerplays.tech/supporting-and-reference-docs/sidechain-flow-diagram-hive