It has nothing to do with either of them. Touch ID does not use enough battery power to make a difference. An upgrade to a new iOS will not necessarily make a difference although you may find may people disagree. The problem is with your individual device. You will need to troubleshooting your device to see what the issue is. You can go to Settings>General>Usage>Battery usage to find out what applications are using the most battery. You may need to reset you device to try and stop any stray processes, or try restoring to a backup.
Restart your iPhone, iPad, or iPod touch - Apple Support
Restore your device from an iCloud or iTunes backup - Apple Support
If those do not help, then restore as new and test without adding any content back. If after a period the battery seems to be acting normal, then sync your content back. If it does not help, then make a Genius Bar appointment to have the hardware checked.