Academically, JHU is a top university and can compete with any Ivy League school. Its courses in international relations, creative writing and biomedical engineering rank among the best in the country in several university guides, and the most recognized courses are pre-medical courses and medical courses for undergraduates and postgraduates.
Outside the medical field, JHU has always been a bit low-key in public cognition and recognition. As others have mentioned, it has no law school, and the business school is still in its infancy. Apart from lacrosse, this is a big event. It doesn't have any famous sports, so you won't often see its name in NCAA.
From the past interaction with JHU students, we can infer that they are as smart and motivated as any famous university students. Many people choose to go to JHU instead of Ivy League schools. If you are lucky enough to go, you may be confident that in the real world, your degree will be highly valued like Stanford University, MIT or other Ivy League schools.
It is highly praised by academics and scientists. The faculty and staff of Johns Hopkins University have contributed to some of the most widely read publications in almost all disciplines, especially those related to health care/medicine, natural and social sciences and global politics. Many Nobel Prize winners and other honorary winners have teacher or alumni relations with Johns Hopkins University.
On the other hand, it has no law school or famous business school, is not a member of the Ivy League (the Ivy League is just a sports league), and does not offer any first-class sports (except lacrosse). Therefore, it doesn't have many famous alumni or billionaires like some other schools.
Although it is a challenge to enter any undergraduate or postgraduate course at Johns Hopkins University, popularity is really important in many professions, including business and law.