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.
The price of ethereum did not just increased significantly as you think, the ERC20 tokens including DeFi really helped ethereum, also is binance coin, binance coin did not just increased significantly like you think, one of the reasons it increased significantly in price is because of the BC and BSC. Did you think pancakeswap exchange just become the first at the time BSC was launched and it supported it? No. I see binance coin for these reasons to be ethereum comoetitor.