I think my 6D may be defective. I have the GPS and Wifi off, and I've shot about a total of 19 photos on the current charge, and with the camera sitting off in my bag for 3 days, the battery is stone cold dead. I'm using the OEM battery that was included with the cam, and another Canon LP-E6 that I picked up from Amazon (not third party seller either, so it's a legit canon battery).
I've had my Tamron 24-70 F2.8 on the camera the entire time. I've read where people have some issues with the 5D3 and third party lenses, so I hope that's not the case, as I love the lens and prefer to leave it on the body...
EDIT~ As an update to my original post, apparently there is a well-documented issue with the Tamron 24-70/2.8 and the newer Canon bodies, like the T4i and 6D, where the lens drains the battery even if the camera is off. Mine battery showed 98% charge, and then after sitting for roughly 2 hours, completely off, it's down to 91%. So I put my Canon 50mm/1.4 on it, and let it sit for 2 hours...and it's still at 91%.
The POTN forum post I saw regarding the T4i said Tamron knows about it and will exchange the lens with one that doesn't drain the battery. I friggin hope so, cause I'm loving the quality on this lens.