Sean Coffey was a powerhouse among plaintiffs’ securities lawyers, touted as the potential new king of securities class actions following the troubles at Milberg LLP and his securing $6.1 billion in recoveries for WorldCom investors.

But last fall, Mr. Coffey, 54, told his partners at Bernstein Litowitz Berger & Grossmann he would quit the firm and try something different—a run as New York’s next attorney general.