Is getting into MSc programs in Europe easier than PhD in US?
Master's education in Europe is largely considered an "undergraduate" degree that follows the bachelor's degree, rather than being the prerequisite for the PhD. Thus, admission to a European master's program tends to be much less competitive than PhD admissions in the US. Now, if you're applying to a top program in Europe, it can be as difficult and competitive as in the US. But the average master's program in Europe has a lower bar to admission, so long as you've done the necessary undergraduate studies considered a prerequisite of the bachelor's degree program.

The rules about what is considered acceptable varies, but a few rules of thumb apply:


In a “consecutive” master’s, which requires a bachelor’s in the same discipline, you need to be able to catch up with coursework in less than one year (sometimes one semester, if the program is competitive). 
In a non-consecutive master’s, you just need to have a suitable bachelor’s degree to enroll.