Functionality of NEO & GAS.
Neo is just a share of the Company. It generates revenue of about 7% per year.
Gas powers the network. You will get payed in Gas if you own Neo.
There are special perks if you own a certain amount of Gas/Neo. (Bookkeeper)

   Transaction speed. Neo can support up to 10 000 transactions/second. Ethereum can do 20/second.

   Languages. Neo supports Java, #C, Python (AI here we go) and many more. They are planning to integrate JavaScript as well (bye bye lisk). Ethereum can do Solidity.