HOLD THE PHONE! Just found the problem.
It appears that there are four Japanese versions of Legend of Kage for the Famicom. Just decided to load up both of our versions in Mesen, and the change is shown on the title screen. Your version (Kage no Densetsu (J) [p1].nes) was copywritten by FMG in 1987. My version (The Virtual Console release), however, says that it was copywritten by Taito Corp. in 1986. Now, quickly looking up FMG and their NES/Famicom releases takes me to where they list some releases with "FMG Pirate" in parenthesis. If that's anything to go by, I guessing that I'm using an official version of the game meanwhile you're using a bootleg copy. And, looking at selection of Japanese Legend of Kage roms, they have 4 different versions listed (Including one titled "Kage no Densetsu (J) (FMG Pirate) [p1]").
Now, with Famicom Wars, there are also four versions of the game available, but all of them are official release.