As a senior in high school, many were faced with the same two options, either to remain in Japan or study abroad for university. I actually went to two universities, that is, I applied two separate times, once during my senior year in high school and another time after I graduated and decided to leave my university in Japan.
I chose to apply to both Japanese and schools abroad. Since my school was based on an AP curriculum, I naturally wanted to study in the United States. In addition, I wanted to study at a university where a liberal arts education was already firmly established. This indicated to me that they could excel at both STEM and liberal arts disciplines. I applied to universities in the US but there were other students who went to Canada, Europe, or Singapore. It depends highly on the student, their goals, and concentration.
A lot of Japanese people have the preconceived notion that to enter a Japanese university you need to work hard but graduating is not that difficult. On the other hand, they say that entering universities abroad is easy but graduating is difficult. I just like to point out that that is NOT TRUE AT ALL. In Japan, you must take the university exam and achieve a high score, which determines your eligibility to enter that specific university. Many study endlessly and go to cram schools in order to achieve the score necessary to get in. This is true even if you want to enter universities abroad, since many universities require the SAT or ACT exam scores. Not only that, they look at your accomplishments during high school including extracurricular activities or volunteer work, as well as essays.