Akuki
Ok this is not going to be a traditional battle. Instead, this is a battle of who can discover the others identity first. Obviously if Light finds out batmans identity first he can kill him with the death note, and Batman can put light in jail. Batman must find this out using only his own resources(no going to doctor fate and asking him to find out where the notebook is). This is set at the point in Death Note where Light has killed L and taken his place, so light has access to police databases.