There is so much confusion on this area that is well justified even among Ts themselves and I have learned the difference in my own education that I'll try to explain (this is in the US only).

In the US the doctorate level psychologist is better trained in the areas of psych testing and research. But for therapy, the education in itself is of little consequence. What is of consequence is the actual training which for all disciplines comes in the form of supervised experience - "residencies" for psychologists or "internships" for Masters level Ts (social workers and MH counselors). Different terminology but both are the same. Psychologists have a longer intern requirement before they can be licensed. So one fresh out of school will have more experience. A licensed social worker and counselor can gain the same supervised experience after they are licensed, and many do. I actually think this is pretty important and probably will speak volumes about how effective they may be.It is hours of supervised experience that matters. A social worker with the LICSW distinction has the same number of supervised hours (i.e. experience) as a PhD. A counselor work up the same amount of experience but the license doesn't change, so this is when I would ask. So in the scenario where 3 Ts have the same amount of supervised experience - paid or unpaid- but different licensure, the quality of their therapy at this point will be about the individual, not the education. Even in advising on meds. Psychologists may have had an extra class in grad school, but that's about it.

Personally, as a future T myself (a MH counselor) I'll be honest and say I'd be wary of a Masters level counselor or social worker who works in solo private practice right out of school. There are always exceptions but that's where I'd make the distinction.

All that said, European standards may be different. Educationally everything is held to a higher standard. A social work license in Europe may mean something different than one here so your concerns could be valid in that respect.