Yes it runs now on its own chain and is being developed well because of the success that it is getting today. I'm also against of comparing these two for now but if ever ETH goes on PoS soon, we'll see on how it will affect the coin.

BNB has a lot of advantage if you're ever trading on their exchange, while having ETH, it also has a lot of use but it's mostly for development and building up a new project. But it seems to be not echoing anymore.