Tough to pick one. Many will work very well. I shot one deer over 400 yards.
Cartridges that work well in my opinion start at maybe the cartridges the 6.5 loonies are all wetting their pants over through the 300 magnums.
Somewhere in the middle, say: 264, 270, 7x57, 7mm-08, 280, 284, 280AI, 7mm RM, 308, 30-06 would all work well (+similar cartridges)
The longest shot I have made on the deer was with a 30-06 with 180 CL’s and that was a little over a half mile. It was a very large buck. I was young and foolish.
If I were to pick one cartridge for deer at 400 yards, I wouldn’t go with the smaller of the above cartridges. But I seriously doubt that I’ll pull the trigger on anything except varmints that far away again.
