There is no new ethereum as binance.The binance chain has remained its own chain and not a competitor with ethereum, they stand alone on their own chains although they deployed the same EVM algorithms but i don't see no reason why they should be in any form of comaprism.
They are indeed competing to each other and the fact that both blockchain has EVM running under the hood further implies that BSC truly intend to take on ETH's position even CZ himself trying to say that ETH is a big boy's chain meaning it's expensive in a condescending remark.
If you see how BSC is eating up ETH's market cap as well you can know that the competition is rather fierce but BSC is actually not really a big threat, now that matic also come to the stage the competition fade even more but BSC was intended to replace ETH from the very start regardless but fortunately people still prefer decentralized blockchain.