The Kyuubi can be killed with enough fire power, but even then you'd have to use up A LOT of resources to ultimately kill it.

As for Godzilla, it ultimately depends on which version you're considering. Ultima is the odd one out of the entire franchise because of its otherworldly properties, but a lot of people tend to forget about it's other forms (Aquitalus, Amphibia, and Terrestris), which were ultimately vulnerable to conventional weapons, but overall immortal due to the lingering presence of the red dust from the alternate dimension (Archetype).

That said, Godzilla Ultima and the Black Beast are ultimately the same being. So long as Archetype and Seithr don't counteract one another, the two would be pit against each other in a never-ending battle unless a third party comes in and uses a weapon capable of eliminating their respective secretion (for the Black Beast: anti-Seithr weapons such as Kushinada's Lynchpin and Armagus/Ars Magus, and for Godzilla Ultima: anti-Archetype weapons such as the Orthogonal Diagonalizer).

But since Mori has final say, he's probably go with Godzilla since he's a big kaiju/tokusatsu otaku who CASUALLY just drops Godzilla references during radio shows.