Do you have the phone set to Eco mode? The quad core processor does seem to suck up the battery when in use, and Eco mode should help some. However, when I am not actively using a phone, the biggest drain seems to be the radios. If you are in an area without 4g, you can shut off 4g and probably get some battery savings on this phone (I do that).
On another android phone, I shut off 3g data, wifi and gps and it doubled my battery life... I could get 2+ days off a charge instead of 1 day. I don't know if the difference is quite as dramatic on this phone since I use it way too much to see how it does without apps (and the screen) actively running.
I have started using Juice Defender and when I am not actively using the phone, it seems to have done a decent job of preserving my battery, I am getting some extra life. It shuts off the data connection, and reconnects periodically to allow for emails etc to be synced. You may want to check out a similar program if short delays on emails etc are acceptable to you. I have also disabled Juice Defender at times to ensure quick responses when I was waiting for a specific email...