Whatever is primarily safe then comfortable and practical for you , your type of weapon and your circumstances. Muzzle awareness being important and being familiar and competent in the operation of the weapon being used.
Having guided a lot of people (lowland) over the years I have experienced most styles of carrying rifle both good and bad.
If someone is behind me I prefer them to carry muzzle up,rifle behind shoulder. Always disconcerting to here metallic clicks and mumbling from behind.
If I am carrying a long heavy rifle, mod,scope,bipod etc I prefer to carry it over the shoulder barrel up.
Otherwise if I am alone with a shortish woodland setup I prefer muzzle up facing forward over the right shoulder. I can hold/ control the the rifle barrel in my right hand and sticks in my left.