Hmm... I went from a custom 4.1.2 ROM on my GS3 phone to a custom TW 4.3 ROM. It seems that the phone Android version would have little or no effect on the watch battery (would effect how extensions might work or not). Have you tried resetting the watch, deleting all the SW2 apps off the phone, and reinstalling? Might also want to make sure you have the most up to date firmware on watch.
Sent from my TouchPad using xda app-developers app
Android devices: Samsung Galaxy S III running CleanROM 8 (retired phone: HTC Thunderbolt running InfectedROM NuSense Eternity); HP TouchPad running OaT CM10.1, Sony SmartWatch 2