Step 1: Concept
Electrical conductance depends on the number of ions produced in solution.
Step 2: Analysis
$CoCl_{3} \cdot 6NH_{3}$ is $[Co(NH_{3})_{6}]Cl_{3}$, which produces 4 ions: $[Co(NH_{3})_{6}]^{3+} + 3Cl^{-}$.
Step 3: Analysis
$PtCl_{4} \cdot 5NH_{3}$ is $[PtCl(NH_{3})_{5}]Cl_{3}$, which also produces 4 ions: $[PtCl(NH_{3})_{5}]^{3+} + 3Cl^{-}$.
Step 4: Conclusion
Since they produce the same number of ionic species, their conductance will be approximately the same.
Final Answer: (C)