According to this review, the theme for Mechani-Kong in KKE was reused for Mechagodzilla. Wikipedia and IMDb, if they can be trusted, say the same thing in their articles for G vs MG II.
It sure doesn't sound like it to me. The Mechani-Kong theme is stylistically similar to the Mechagodzilla theme Ifukube used in Terror of Mechagodzilla, but they're clearly different melodies. (Masaru Sato did the first Mechagodzilla film.) Maybe someone just confused the two due to their similarities. I needed to listen a couple of times to make sure they were different. But the GvMG2 theme is quite different from either.