Depends on the nature of the breach, if its a flaw in the software itself, then perhaps exploitable both in the hosted offering and BYOC offering, though perhaps the BYOC aspect gives a bit of "security-through-obscurity" and less discoverable as a target.
I was thinking the same thing on security-through-obscurity.
a hacker might know how to hack your service, but they'd have to find it first.
Good point, there are of course different levels.
I was thinking of a fully private deployed within the customers cloud account connected to the software provider via Private Service Connect or PrivateLink and then either only available inside the customers private network or only via their own firewall. The point being that it's not publicly exposed.