I can talk about PhDs in the UK, I have less knowledge of the rest of Europe, but I know that it is not similar to the US.
In the UK, you specialize early in a subject, and your education is therefore narrow and deep. In the US, you specialize later, and your education is therefore wide and not so deep. It's changed a little (but only a little) since I was in school, but at age 13, I dropped all but 5 subjects plus math(s) and English. I chose the three sciences (chemistry, biology, physics), geometrical and engineering drawing, and French. If you chose not to take any science at age 13, you were not going to be studying any science at university (I think this is changed, so you are required to take at least some sciene). Hence I have studied no humanities since I was 13. At age 16, you reduced again to three subjects - you are interested in science, people typically studied physics, chemistry, biology, or perhaps swapped the biology for maths. When I teach psychology undergraduates, health science undergraduates, or health professionals who are taking postgraduate courses, they will typically have done no math(s) since the age of 16. (This is a challenge, as I teach them statistics. If they knew anything about algebra, they've forgotten most of it. They will deny ever having been taught calculus [and that's true, they probably have never studied it]).
At 16, I chose biology, psychology and environmental science. (Env Sci is, or was, essentially applied chemistry and biology, with a bit of geography).
In the UK, you go to university to study a subject, and that is what you study. There is no concept of picking a major. If you want to change your major, you usually start again. (In my first year, I studied two subsidiary subjects for 50% of the time, after the first year, I did nothing except psychology courses.
When I graduated at age 21, I had a degree in psychology, and I'd been studying psychology for 5 years (and psychology had made up almost 2/3rds of what I'd studied from age 16).
The PhD has also changed, but in the UK at the time, the purpose of the PhD was to write a dissertation. That was the only requirement. In the US, there is the idea of PhD-ABD - all but dissertation. In the UK, this would make no sense, there is no requirement for a PhD except for the dissertation. You start, and on day 1 you work on your dissertaion. On day N (where N is quite a large number) you submit your dissertation, and you're finished. This is changing, or has changed so that there is a coursework requirement for a PhD; but in the US people talk about taking courses in departments outside their PhD subject. This is very rare in the UK - you take courses offered by your department, and you take the courses you have to take, no more. British PhD dissertations are considerably longer and more substantial than American PhD dissertations.
In comparison to an American student, a UK graduate in (say) psychology seems to know more psychology. But they know a lot less other stuff. In the US, it seems (to me) to be common to do a master's degree (or even a PhD) in a subject that you did not major in at undergraduate. For example, I've known people with a degree in economics or sociology who take a master's degree in statistics. This would be very rare in the UK, you would simply be too far behind everyone else on the course. (Many years ago, I applied for a master's course in applied statistics (an early online course) - I'd published papers on statistical methods in psychology, and had a PhD on statistical methods in psychology; I was rejected because my background was unsuitable.)