Both sides have the special arc design to support and cradle your neck. The only difference is the height. While it essentially comes down to trial and error and personal preference we have also had a chiropractor trial the sleep positions and offer suggestions.
This is what they had to say....if you sleep on your side, the higher side will offer the most optimum support for your neck and shoulder but also offer the correct thoracic alignment. The lower side is perfect for back sleepers allowing their bodies to be in a neutral position. It is not recommended to sleep on your tummy for various reasons including the strain on your neck when having to stretch it so far to the side however if this can't be avoided the lower side is great because of the head hollow and you may be able to use this pillow to train yourself out of tummy sleeping.