Although about the same weight as the 600/4 and the 800/5.6 the extra f stop and shorter length of the 400/2.8 should make it easier to handle than the other two behomoths!!!!
The 400 f/2.8 is about the same to handle as the 600 f/4, although the extra focal legth makes it more difficult to hand hold it steady
Biggest problem with the 600 f/4 is that the minimum focus distance is a bit on the long side, whereas the 400 focuses much closer
Here is a handheld photo of a polecat
Camera Model Canon EOS-1D Mark IV
Shooting Date/Time 31/03/2012 14:51:29
Shooting Mode Manual Exposure
Tv( Shutter Speed ) 1/400
Av( Aperture Value ) 2.8
Metering Mode Spot Metering
ISO Speed 160
Auto ISO Speed ON
Lens EF400mm f/2.8L IS USM
Focal Length 400.0mm
AF Mode AI Servo AF