I don't think BNB will overtake ETH, BNB have a goof improve but it's not anough because ETH is more popular and have a good platform and community.
These are different cryptocurrencies, and I do not see the reason for their competition right now. Although Binance attracts with the decision to burn their tokens regularly to support BNB, I believe that Ethereum has got better support. Take into account that most Dapps work oin Ethereum (they say, over 87% of them), so ETH is still better for many people than BNB, which is also a relatively new token.
Eth has more long years to influence the market to be sustainable, however BNB has the capability to be more promising like eth but it's not the perfect time yet. If BNB has more new projects to offer to the community like having its new contract, and those projects will provide us more opportunities to take part of it, I think it has more potential to compete for the best market that could overtake other coins not just with eth. Hopefully there's an ICO token that's supported by BNB in order that it could increase adoption.