Supersonic... because those boats might outrun a subsonic missile /s
It won’t need to outrun the boats, but just the anti-missile systems protecting it.
An aircraft carrier has a snowball’s chance in Hell of being able to swat out a supersonic missile locked onto it. Imagine a rainstorm of these...
They are working on a hypersonic version, also!
You;re almost right. Not outrun, outfight.
With a subsonic cruise missile the CIWS defence has to knock it out between 4km (when the fire control can first identifty it as a threat) and 1Km (after than, even if you destroy the guidance or flight control, the "dead" bird may still make a ballistic hit) that's about 10 seconds for a subsonic missle.
Now make the missile Mach 3. Far engagement range is the same, close engagement range moves out to 2Km. So 2/3 the engagement window at 3-4 times the speed. Time to target and hit goes down to 2 seconds.