How does Qubes OS compare to using a “live CD” OS?
A live system is monolithic, i.e., it has no compartmentalized networking (sys-net), USB (sys-usb), sound (sys-audio), graphics (sys-gui). Any successful attack on any of these components may result in Game over™, whereas Qubes should save you from that (assuming you use it correctly).
Concerning privacy, neither Fedora on Qubes, nor live Fedora can provide a reasonable privacy*, due to browser fingerprinting, see this and this.
*except if you are using Tor Browser, but Whonix also uses it and is generally more secure.
Perhaps relevant: Qubes VS Tails.
Less relevant: QubesOS vs OpenBSD Security.