Right now, in terms of savings, it is better to use BNB. It is cheaper and faster than ETH transactions, but I think if BNB has the same number of projects as ETH, the blockchain might not be able to handle the load. In general, I don't understand the hype around Ethereum. I guess there is a lot of money and serious people behind it, there is no other explanation why people use it.
True, most tokens have moved to the BNB to take advantage of the BNB ecosystem. Guess there will be a 'pass down' where ETH become more like BTC, a monolith in term of price while BNB become more like ETH a few years ago. Since the next ETH PoS is around the corner so unless the ETH 2.0 did address the fee problem, they could turn back the table.