Simply a matter of preference. Muzzle down on the left is sometimes called "African carry" and muzzle up on the right, "American." Some people switch between them to minimize fatigue.
In American carry, you hold onto the sling to make sure the rifle stays in place. In the other method, you hold onto the rifle. Either is equally quick when it is time to put the rifle into firing position. But note that either muzzle up on the left, or muzzle down on the right, is not as convenient, for a right-handed person, when it is time to put the rifle to use.
A reason for arranging the wide part of the strap to the rear is that it puts the wide part aft when you rig the cobra sling as a firing sling, "CW" fashion. (That is moving the rear sling attachment from the aft swivel on the rifle to the middle swivel so that you can use the sling to steady your firing position.) It is more comfortable if the wide part of the sling is around your forearm when you loop up.
These matters and more are gone into in Jeff Cooper's book,
The Art of the Rifle, which is one of very few shootin' books I recommend.