A degree holder without professional quality is better or a professional without degree?

Agreed to the reply of Petter Scott.

It is further added that Professional means: expert, specialized, skilled, trained, and proficient etc AND

Quallity means: excellence, superiority, class, eminence, value, and worth etc. So on basis of these meanings a Professional even without a degree is better than a Degree holder without having the above things. However, a degree holder if given a chance, can gain the things mentioned above. 

If you use professional in the context of someone who is proven, good at their job, diligent, then why would they need a degree? If you are looking for employees with potential then maybe think about post graduates at entry level, they have proved that they can absorb knowledge and should be receptive to new ideas and training.