Because the 6D camera has an internal GPS and even when (on the menu) it is turned off: it still updates the satellite positions. This updating causes the battery(s) to drain and can go dead in a matter of days. The battery drain is contingent on the updating interval time that is chosen.
If you have a GP-E1 or E2 on your 1D, they may operate differently...I have no experience with them. The 6D GPS is internal not external like the E-1 or E-2, which no doubt could be the difference, especially, if you experience no battery drain.
Do you have a friend or acquaintance that has a 6D.? You might discuss the matter with them.
I basically buy Canon Products for their quality. I recently purchased a TAMRON 24-70 f2.8 because Canon's 24-70 and for that matter Nikon's 24-70 do not have stabilization. Tamron's 24-70 has their own form of stabilization. It works very well.
I know nothing about 3rd party battery grips.