BitShares uses the same Graphene platform that Steem uses. So, essentially, your private keys are your responsibility, and they are stored client side (e.g. in your browser).
For historical reference, Dan Larimer built BitShares then Steem and now he's building EOS.
Steem's cryptocurrency is built specifically for their platform so it's understandable for Steem. I still think there is way to much hype around EOS, so that is actually a strike in my book.