China's President Hu Jintao landed in Washington for a summit that will help to define a new relationship between the world's longtime superpower and its rising Asian rival, at a time when their bonds have been frayed by mutual suspicions and an ideological gulf.

Since Mr. Hu last visited the White House in 2006, his country's influence has surged and its relationship with the U.S. is now widely recognized as the world's most important bilateral matchup. In some ways ties have strengthened, as in the growing trade and business...