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.
Ethereum is far more supreme than BNB. Its decentralisation and smart contracts are way more trustful compare to BSC. The edge with BNB network is that it has less transaction fee compare to fully congested Ethereum network.
BNB and ETH both will be successful. But I am more optimistic about BNB, because Binance is the largest exchange and the team is excellent.
Being the largest exchange doesn't guarantee your funds. As far as I know, Mt. Gox exchange was the biggest before yet it was hacked by unknown entities. Watch out.