I don't see Ethereum as the opponent to EOS. The last project by Dan seems to be far superior to the buggy Ethereum one.

I think the competition will be between EOS, Cardano and Aeternity, instead. All three are born with the main goal of fixing the problems Ethereum is having. Ethereum is trying to fix its own problems, but it is very hard to do it while, at the same time, keeping the compatibility with old platform.