Janeway does have the authority to order Tuvok to his death but doesn't have the authority to do so with Neelix. I'm not so sure whether she had the legal authority to order Tuvix to his death.
Even if she had the authority to (which I won't argue), that doesn't mean it was the moral thing to do. Also, under the Starfleet charter to seek out new life, even if she had the legal authority to execute Tuvix, that doesn't mean it was very principled to kill a new form of life or species.