If a VM running inside QEMU is able to compromise QEMU's code, it then runs with the privileges of QEMU on the host. The host, the regular OS running QEMU, is colloquially called "the hypervisor." And in most production virtualization setups, there is nothing of interest on the host other than some QEMU processes itself, i.e., anything valuable on the host is perfectly well accessible to QEMU, and therefore to malicious code that has taken over the QEMU process.
The "hardware acceleration" that helps QEMU emulate a computer operates in root VMX and non-root VMX (when actually executing guest instructions) modes. When operating in root VMX mode as a supervisor, it has approximately the highest privileges in the system (ignoring SMM), as it is operating in host ring 0. QEMU runs in host ring 3, making it a typical user mode process. If you manage to compromise QEMU (and only QEMU), you have only escaped into host user mode. In that case you haven't compromised the hypervisor, merely the virtual machine monitor.
If, on the other hand, you manage to compromise KVM (or vhost) you could reasonably claim to have actually compromised the hypervisor.
Type 2 hypervisors make this generally much uglier than type 1, but it's reasonable to say that the hypervisor in a type 2 deployment is limited to the kernel component rather than the user-mode VMM.
and MINIX in case of Intel :-)
In a well configured KVM instance QEMU obeys the principle of least privilege as much as possible, that is it can only access the resources it needs to do its job.
In practical terms, this means QEMU is confined (via SELinux, cgroups, Unix permissions, seccomp) to only access resources for the VM it is running; taking over QEMU does not give you access to "anything valuable on the host".
Of course, having remote code execution in QEMU is awful; it can be a base for exploiting a kernel vulnerability to get root access. Luckily this bug would not be exploitable in a production setting.
And I think that there is no common configuration of OpenStack or libvirt that assigns unique access control labels per VM. Every qemu runs with the same privileges, ergo one exploited qemu can laterally attack another. (But maybe there's something nifty I'm missing?)
(Agree that for the use case of desktop virtualization, a good SELinux config can keep it from accessing your browser cookies.)