I have a 6D and a 5D Mark IV. I haven't used the 5D enough to profile its battery life, but in my experience with the 6D, GPS causes maybe 15% battery drain per day. And with the 5D Mark IV, it should use much less, assuming you take advantage of the new "mode 2" behavior that turns GPS completely off when you switch off the camera.
So in a three-hour shoot, you should have lost maybe two percent of your battery life to GPS. Assuming the camera really gets 900 shots on a battery with GPS off, it should have been able to shoot something like 880+ shots in that time even with GPS turned on.
So you're getting almost a factor of four fewer pictures than I would expect to get on a properly functioning camera. IMO, the only way those numbers make sense is if either:
- You left the camera turned on in your bag for 2–3 days prior to the shoot
- The lens you had attached was a buggy/defective one that drains lots of battery power
- You left the shutter button halfway down almost the whole time (IS and AF running continuously)
- You did the entire shoot using live view mode
- You also shot a lot of video footage
- Your preview time is set to something absurdly long
- One of your flash cards has a nearly dead short across its power pins
- Something is wrong with the battery
- Something is wrong with the camera
- Something is wrong with the charger
And most of those issues should have happened with your Mark III as well, assuming all else was equal. And if you were used to shooting everything in live view mode, your battery life would have gotten dramatically better thanks to DPAF. So my guess would be that your new battery has a defective cell in it.
To rule out other possibilities, though, I would suggest trying the following things, charging your battery each time, and recording the charge percentage in the Battery Information menu afterwards:
- Leave your camera turned on and idle for three hours with different lenses connected.
- Leave your camera turned off (with each of those same lenses).
- Repeat with different SD cards and different CF cards using one of those lenses.
- Repeat at least one of those tests with a different battery.
- Repeat at least one of those tests with GPS fully disabled.
That will at least help you narrow down the source of the unusual battery drain. If the problem is the battery, contact Canon, as I'm sure they'll be eager to get their hands on a battery that failed so early in life. If you can't reproduce the problem, then who knows. For that matter, it could even be a software bug in calculating the remaining charge for older batteries.
In other words, ¯\_(ツ)_/¯.