Well, perhaps obviously, professional suggests more suited to a working environment than a home environment, and premium suggests superior, perhaps an enhanced or more luxury alternative.
Rather than limiting yourself to 'Professional' or 'Premium', you could come up with a word that expresses the advantage of the commercial version.
e.g. speedy, unlimited, unbreakable, secure, supported, etc.
I'd use professional if you want to sell to commercial users and have the other version for home users, and premium if you can't think of a single more suitable word.