When you talk about trusting a coin, you have to look at different achievements of the project working with the token or coin, the background and level attained. To me, Ethereum is a base token and can't be compared to BNB, unless there's better and strong competition from BNB. I go with Ethereum.
I also believe that you can not put these two coins in the same row, since they have completely different functions. BNB is the coin that created exchange Binance and the value of which is very closely related to the functioning of this exchange. And Ethereum is the basis for most cryptocurrency projects.
I guess BNB is already competing with ETH, they have their own chain now, it can't be denied that BNB raise their ICO creating a token in the ETH smart contract but BNB has a plan, they want to compete so they left ETH and build their own.
As of now, they have a decentralized exchange, that would compete with ETH DEX, and maybe soon more development will happen within BNB's project.
This coin is literally not an exchange coin only, their achievement is quite impressive.