BERLIN—In October, Amer sold all his belongings in Syria and took his family to a safer life in Germany. Four months later, he wants to return to a country still at war.

Once in Germany, Amer discovered an unexpected reality: Instead of the small house he was hoping for and money to help him open a business, he was given a bare room in an old administrative building turned into an emergency shelter. Now he is packing his bags again.

“I came to Germany because everyone was saying it was heaven. Now I regret that decision,” said the 30-year-old from Damascus.

Last year, 1.1 million migrants—mainly Arabs, Afghans and Africans—came to Germany to escape war and hardship, many of them risking their lives to make the dangerous journey. Authorities have scrambled to accommodate the influx and Chancellor Angela Merkel is facing growing public discontent, especially after the alleged role of foreign-born men in the mass assaults in Cologne on New Year’s Eve.

But many who arrive find the country doesn’t match their often inflated expectations. They balk at modest benefits, poor job prospects, and harsh treatment at immigration offices, and voice other complaints ranging from bland food to Germans’ open attitudes about sex.