This question has another question in itself. What do you mean by product design? If one is talking about product design in relation to the physical products than the answer is UX has more better scope because UX is about user experience. It will be applicable for both physical and digital goods.
If the question is specific to UX for software services and UX for software product than there is no much difference in both. Services deal with requirements from client and freedom of design will be there sometimes and may not be sometimes. If it is about UX for a digital product like Adobe, anti virus etc then the scope of UX is huge and designers will get lot freedom to show their potential.