We're big supporters of Ethereum, our initial motivation was to incorporate an Ethereum-esque Proof of Stake model atop a modified version of Bitcoin. However, Bithereum itself is a fork of Bitcoin, and has no resemblance to Ethereum in terms of smart contract functionality, and is naturally a peer-to-peer payment system. Our main difference comes from the network rewarding those who run full nodes, unlike most Bitcoin derivatives, as we feel running a node is just as (if not more) important as mining. We call this Proof of Uptime, which is a term/system we created ourselves, and you can read more about that here: https://medium.com/bithereum-network/bithereums-proof-of-uptime-v2-0-69da7c1ca17