Both blockchains have the same features and are identical in every way up to a certain block where the hard-fork was implemented. This means that everything that happened on Ethereum up until the hard-fork is still valid on the Ethereum Classic Blockchain. From the block where the hard fork or change in code was executed onwards, the two blockchains act individually.
Bitcoin is a digital asset designed to work in peer-to-peer transactions as a currency. Bitcoins have three qualities useful in a currency, according to The Economist in January 2015: they are "hard to earn, limited in supply and easy to verify." Per some researchers, as of 2015, bitcoin functions more as a payment system than as a currency.