CAIRO — A huge demonstration on the first anniversary of the Egyptian revolution turned into a contest on Wednesday between Islamists and other activists over whether to celebrate the ouster of President Hosni Mubarak or to rally against the continued rule of the generals who took power.

Declared a national holiday, the occasion brought out teeming crowds in cities across the country, including an estimated 100,000 demonstrators packed into the revolution’s symbolic center in the capital’s Tahrir Square and the surrounding streets. The outpouring was as large as any during the original uprising. But the spirit of unity gave way to new divisions: Islamists against liberals, political winners against losers, dealmakers willing to compromise with the military against activists demanding its immediate exit from power....