Studies have shown that horses have lower heart rates when facing backwards in a horsebox. They seem to find the experience less stressful and can engage the muscles of the hindlegs and hindquarters to buffer the effects of braking.
When facing forwards, they tend to hold their heads higher, which puts stresses on the neck. A horse travelling with his head high, or in a fixed position over a locker, or with insufficient space to stretch his neck out, may be very stiff after unloading. Any existing neck issues will be exacerbated by travelling in this way.
A large horse may prefer to travel without the partition so that he can stand diagonally or place himself as he feels most comfortable.