FELCSUT, Hungary — The Pancho Arena stands about 20 yards from the country home of Viktor Orban, Hungary’s prime minister. The professional soccer stadium has a heated pitch, a museum, a spotless medical clinic and 3,814 seats, double the population of the surrounding village.

In the same county, the biggest public hospital, the St. George, is flagging. On a recent night in the emergency ward, the women’s bathroom had no soap and the men’s room had no functioning urinals. Two doctors struggled to treat an overflow of patients, with 30 still waiting past midnight.

Gleaming soccer stadiums. Decaying hospitals. The contrast reflects the priorities of Mr. Orban, who has become one of Europe’s most powerful far-right leaders by presenting himself as a nationalist champion of ordinary Hungarians and a scourge of European elites.

Yet ordinary Hungarians have suffered most as the country has plunged in European health ratings and many doctors have departed since Mr. Orban took office in 2010. Health care was badly managed by prior administrations, but Mr. Orban has overseen a drop in government health care funding as a proportion of national economic output.