I looked it up, they both don't:

• The Bit Gold p2p transaction log is based on network addresses.
• B-money design A is assuming that you have perfect communication which distributes the same transaction to everybody synchronously and doesn't need it.
• B-money design B is uses “servers” to keep track of transactions. Setup of new servers is limited by requiring money to create one.

The real interesting new thing about Bitcoin is not the scarcity of the coins, but the decentralized ledger. The coin scarcity is a side effect.