If it is possible for them to fight, I can imagine a scenario like this one.
SCENARIO-
-it is set in a Amalgam universe of Death Note and Code Geass
- the Britannians have JUST taken over Japan, renaming it Area 11, and reducing the Japanese to live in slums
- Lelouch creates the Zero disguise after gaining the Geass power from the powerful immortal witch C.c the Geass allows him to control anyone he stares in the face, to take down his father, the Emperor of Britannians who murdered his mother, as well as liberate Japan to make it safe for him, his friends and his sister to live in, he has formed the Black Knights to help his cause
-Meanwhile, Light Yagami, an eleven who lives in a Britannian enclosure, due to his father's excellent work as a police chief finds a Death Note, he is soon confronted by the Shinigami Ryuk and becomes "Kira" set on ruling the world by first killing the entire Britannian royal family, however Zero halts his plans, seeing Zero to be a threat, Kira releases a recording challenging him,
and so the hunt is one, who finds who first? who will win this game of cat and mouse? who truly is justice??
- The Stegman