The update is a security patch that was released to stop unlocking rooting the device and the ability to unlock the bootloader. Therefore it should have no affect on battery life but you have to remember, OTA updates aren't perfect and sometimes will cause "side effects" to your phone. If you phone isn't getting as good battery life as before, flash it back to stock go from there. It isn't difficult to go back to stock OS, you don't need root or be unlocked, all you need is to know how to read instructions.
My opinion in this would be to restore back to stock, root you device and then disable the background application that will send OTA updates to your device. As long as you don't side-load apps on your device the chances of having an issue with the security exploit are slim to none. If you don't want to go that route, you can try calling Verizon and voicing your opinion but since this OTA is no new, even if they give you a new device the actual device won't be running the newest software and you will get the OTA anyway.
Try to troubleshoot the problem as well. Download apps like CPU Spy and GSAM Battery to give you a better idea of what is eating your battery quicker.