For the past few years, much of John Ricco’s job has been taken up by listening to clients bemoan how frustrating their careers have become and how few opportunities they see for advancement. That would be OK for a therapist, but Mr. Ricco is a recruiter who specializes in the financial-services field.

Fortunately, after a long dry spell, financial firms are finally hiring again, and Mr. Ricco’s conversations are taking a sunnier turn.

“Everybody is anticipating a good year ahead,” said Mr. Ricco, a partner at the Atlantic Group. “Firms are looking to expand, and they’re going after people. Jobs are coming back.”

That said, the employment situation on Wall Street is quite different from the upswing that ended abruptly in 2008. The most desirable places to work aren’t the big banks, but rather private-equity firms such as the Carlyle Group and hedge funds like Fortress Investment Group, Mr. Ricco said. And although these money-management firms are staffing up, the major investment banks, such as Goldman Sachs and Morgan Stanley, are moving more jobs out of the city for -lower-cost locales like Salt Lake City and Tampa, FL.

Signs of further retrenchment emerged last month, when Bank of New York Mellon said it would put its historic headquarters building in lower Manhattan up for sale and move many of the people in it to a smaller building nearby.

So far, only about a quarter of the more than 30,000 securities-industry jobs that vanished from New York after the financial crisis have come back. That’s a worrying trend for the city, where better than one-fifth of all private-sector wages come from the financial sector. Wall Street jobs, in turn, support a host of others, from lawyers and real estate agents to personal trainers and bartenders.

Even though asset-management firms are adding people, there are questions about whether they can grow enough to offset declines at the investment banks. The Carlyle Group, for instance, employs only about 1,400, and Fortress has about 1,100. BlackRock, the world’s largest money manager, has about 11,000 employees—merely one-fifth as many as Morgan Stanley.