it's hard to even say ETH is "competing" with bitcoin on equal footing, it would be the same as saying USA and a developing country are in the same conditions and economical condition, which is false.
ETH is growing, I can't deny that, but I don't think it's even close to even over-taking bitcoin, it's still impacted like this with bitcoin SegWit, I think this shows how much it is just an off-shoot of bitcoin, and still completely dependent on bitcoin price.

Banks are a fundamental and critical part of the financial system and is very important, I don't think bitcoin can make these disappear in a day or two and it would be a process of years if it ever happened.
Banking system would change with the blockchain system IMO, but not banks themselves disappearing, and it would still be the same (people open accounts, deposit, bank lend to merchants, pay interest).