Front and rear both lock left and right together at their respective ends. Center locks the rotational speeds of the driveshafts together. In a corner there are 4 different rotation speeds occurring. The tighter the turn, the more this comes into play. Notice you leave 4 separate tracks in the mud/snow/sand when cornering this shows that your tires are traveling different paths and therefore different distances. Try locking your CDL and making a full lock turn in reverse on a high traction surface (clearly not what we're coving above). You will very quickly feel your driveline bind up. If you push it, one of two things will happen, a tire will break traction or a mechanical failure will occur. The diff exists for a reason.
I'm not interested in further interweb argument so I'm not touching the engine braking comment.
^^^^^ This is correct....and requires no argument.
Many folks misunderstand the relationship between the T-case being locked (driveshafts forced to turn at equal speeds) and the differentials at the axles (open diff still operates as before, locked diff acts the same as a locked T-case). And then there is the indisputable fact that the front tires take a different 'track' than the rear tires in a turn (meaning the front and rear tires are turning at different speeds as well as the outboard tires on each axle).
The physics @RedHeadedStepChild alluded to is solid information. HOW this manifests as 'handling' in snow or other low traction conditions can vary widely.