So this may be a very noob questions but I trying to wrap my head around how storing BTC in my Bitshares wallet as open.BTC is any better than storing on an exchange.
It isn't. At least not a lot.
OPEN.BTC is an IOU issued by OpenLedger, a privately owned company located in Denmark. The OPEN.BTC balance shown in your bitshares wallet is similar in nature to the BTC balance shown in your account on a centralized exchange.
Who owns the private key to that open.BTC wallet address?
Is there a way that I can get the private key to this open.BTC wallet?
You own the private keys to your bitshares wallet. You can't use these to access actual Bitcoins. You can only use them to handle your OPEN.BTC. You should also be able to retrieve the private keys somehow using the UI.
OpenLedger (the company) owns the private keys controlling the actual Bitcoins. You can't get access to these.