I had 6D 1 one month ago and no problem with battery. LCD using normally in wedding work. I can't take 1200 shoot (6D2), maybe 200 photos only. I'm thinking about battery, something is wrong, buy new one and test both.
I have new one 6D II and same problem with battery life. GPS wifi are disabled. 10 min 3% battery down. I must buy grip and new battery then test second battery. I will write here after results.