Light vs. Lelouch

For whatever reason, Light Yagami/Kira from Death Note is pitted against Lelouch vi Britannia/Zero from Code Geass.
Light is allowed his Death Note, the Investigation team (Who temporarily set their sights on Zero), Ryuk (Who, as always, only gives vague hints), and Misa Amane. Lelouch is allowed his Geass, the Black Knights Zero Squadron, and C.C..
Neither knows the other's identity, and only have a basic idea of who the other really is. (I.e. Lelouch think Kira is probably on the Investigation Team, Light thinks Zero is probably a student)
Never mind the fact that one can't exist in the other's universe. Who wins?
Light is allowed his Death Note, the Investigation team (Who temporarily set their sights on Zero), Ryuk (Who, as always, only gives vague hints), and Misa Amane. Lelouch is allowed his Geass, the Black Knights Zero Squadron, and C.C..
Neither knows the other's identity, and only have a basic idea of who the other really is. (I.e. Lelouch think Kira is probably on the Investigation Team, Light thinks Zero is probably a student)
Never mind the fact that one can't exist in the other's universe. Who wins?