I know everyone is talking about LTE eating juice and whatnot, but I don't think that's the problem. Neither is syncing or whatever. Go to Settings->About Phone->Battery->Battery Use. What's eating up a majority of your battery? At least for me 65-70% of usage is the display. Based on that, it would seem the #1 thing you can do to save battery is turn down your screen brightness. I've got mine set at around 30% or so.
That's not the case for me. I turned off GPS, BT, and Wifi, killed all tasks using Advanced Task Killer. I didn't even turn on the screen for about 3.5 hours, and my battery went from 100% to 48%.
But now that I've been reading this thread, I think I'll try uninstalling the Task Killer. I turned off the sync for News and Stocks, simply because I didn't want them. Now I see that it may help with battery life.
I hope this works, since this is the last day I'll be able to return the phone, if it comes to that.