In \([\text{Ni}(\text{CO})_4]\), nickel is in the zero oxidation state and has a \(3d^{10}\) electron configuration, leading to a fully paired electron configuration, making it diamagnetic.
In contrast, in \([\text{NiCl}_4]^{2-}\), nickel is in the \(+2\) oxidation state with a \(3d^8\) electron configuration. The chloride ligands are weak-field ligands and do not pair up the electrons, resulting in unpaired electrons and a paramagnetic nature.
Thus, the correct answer is:
\[ [\text{Ni}(\text{CO})_4] \text{ is diamagnetic and } [\text{NiCl}_4]^{2-} \text{ is paramagnetic.} \]