Ethereum and Cardano will both be forced to innovate and improve based on their competitors weaknesses. Cardano has considerably lower fees than Ethereum. Ethereum has huge dApp ecosystem, Cardano has a small dApp ecosystem. Cardano is more decentralized than Ethereum. Ethereum is proof of work, Cardano is proof of stake. Asking for one of these cryptocurrencies to die is shooting yourself in the foot. The best case scenario for us is the coexistence of both the two crypto giants.
How to Mine Cardano
You can't mine ADA. You can however receive staking rewards that pay you in Cardano for holding your ADA in a stake pool. You can stake on Cardano's native wallet Daedalus on your computer or you can use Yoroi app on your phone.