Ethereum Vs NEO. Ethereum is current rank #2, while NEO is rank #13 according to coinmarketcap.com.

1. NEO and Ethereum are both blockchain projects specifically designed to host smart contracts, ICOs, and DApps in a decentralized manner.
2. Their respective blockchains are fueled by crypto-assets (GAS in NEO, Ether in Ethereum).
3. Both the projects are open-source, Turing complete, and have ample community backing with great, responsive teams.

For me, NEO and ETHEREUM main project is about Smart Contracts, like for ICOS and DApps.  And while you are holding NEO in your NEO wallet, you are earning GAS from NEO, which is using for as fee for sending NEO/any TOKEN under NEO. And for my own experienced, transaction fees in NEO are much cheaper compare to ethereum. That's why I am holding some NEO now so that I can earned GAS while holding it to my wallet without doing anything.

Source: Coin Sutra – The Community of Cryptocurrency Lovers.