If you mean trust in the sense of if those projects are trustable and no scams than i definitely trust both of them.
If you mean which project i like more then i would say ETH.
Binance is a good exchange, but they clearly try to take over the whole cryptocurrency space more and more which is dangerous.
Just look at how they advertise for their own projects now on coinmarketcap now that they bought it.
Both coins have performed well over the course of their lifetimes. But evidently, people trust more ETH than BNB because it's one of the oldest cryptocurrencies in existence. Not to mention, ETH brings active development and innovation with decentralization in mind. It may have its flaws (such as high fees and slow transaction confirmation times) but its level of security is beyond compare. No matter how scalable BNB is, it'll never be able to overcome ETH in mainstream adoption. Each cryptocurrency will serve its unique purpose in the mainstream world. I guess BNB will work best for businesses and corporations looking to launch ICOs to the general public, while ETH will work best for the average person looking to participate in decentralized banking (mainly "De-Fi"). Choosing one type of cryptocurrency from the other will truly depend on the person himself.
All in all, Binance seems to have large prominence in the crypto/Blockchain industry. The fact that Binance controls the crypto market, should keep us alerted about the industry's level of decentralization. It could set a dangerous precedence for crypto as we speak. BNB being within the top ranks in market cap, shows us Binance's rise to power in just a couple of years since its inception. In just 3 years time, Binance has built its crypto empire. There could be more to BNB than meets the eye, as Binance continues to patronize it. With a high-throughput blockchain and its own decentralized exchange, BNB could appeal to the business sector eventually leaving ETH in the dust. The latter (ETH) will end up being used by everyday people while the former (BNB) will be the top Blockchain network of choice among businesses and corporations alike. This translates to ICOs, STOs, and IEOs, transitioning from the ETH blockchain to the BNB blockchain in the not-so-distant future. No matter what happens then, ETH will always be one of the most trusted cryptocurrencies on the market by everyday people. Just my opinion