In case of Eos, you need to own the tokens to run smart contracts on the network (mire you have, more % of processing power you get).

In case of Ether, besides being used for transaction fees, it will be used for providing security/governance (token holders kind of voting on what the next blocks are), but also as an underlying store of value (e.g. as a collateral for tokens pegged to fiat currencies - see MakerDAO)