Quote Originally Posted by Mr. Nosebleed
KH1: Fight theme for the End of the World.
KH2: It's the battle theme for Roxas' deep dive (choosing weapons).

I had never noticed it was in each game until you mentioned it.
Don't you mean Roxas' Awakening? I thought Deep Dive was referring to the dark city and its battle shown in the Deep Dive video for KH Final Mix.