I haven't seen the type of drain you are talking about, but I can confirm that my battery life with LTE does not compare to my iPhone 4S w/ 3G. The iPhone 4S could sit idle all day and still be 95%+ battery life at the end of the day, even while on the cellular network, the iPhone 5 is 70%+ battery in the same situation.
Two things to try:
When I got my phone, I noticed poor battery life as well, I let the battery drain down to 5-10% and then I let it charge fully. If this does nothing, check your Usage and see how the phone Usage under Settings->General->Usage compared to Standby. Mine is reporting 2.5 hours Usage and 7 hr 51 minutes Standby. If the Usage and Standby are very similiar, this means that something is causing your device to not sleep properly. You can try to delete and re-add your email accounts and turn off notifications to see if something if causing a problem. If not, you may need to restart the device from scratch (Settings->General->Reset->Erase All Content and Settings) and reconfigure it (when doing this, I recommend you configure from scratch and not restore from a backup from the same device or prior iPhone model)
If you're in a low LTE signal strength area where signal keeps bouncing off LTE, this will result in excessive battery drain, although I don't know whether or not it would be equal or not to what you are reporting since I have never attempted to measure this.