Steve from All About Windows Phone did some testing by tracking his Lumia 1020's battery life for the past 6 months and found out that the combination WP 8.1 official + Cyan provided the best battery life.
See here Charted: Windows Phone 8.1 official/Lumia Cyan has best battery efficiency
See here Charted: Windows Phone 8.1 official/Lumia Cyan has best battery efficiency