But the common interests lately have been overshadowed by an inability to reconcile a bitter, centuries-old history. This was on display last year when a planned Japan-South Korea intelligence-sharing pact fell apart at the last minute amid a political outcry in Seoul.
Things have gotten so bad that South Korean President Park Geun-hye and Japanese Prime Minister Shinzo Abe, both scions of powerful conservative political families, won't even talk to each other. Abe and Park have yet to hold a summit meeting in their first year in office, usually a high priority for both countries.
When U.S. Defense Secretary Chuck Hagel broached South Korea-Japan ties on a recent visit to both countries, he got an earful from Park on Japan's alleged whitewashing of the past.
Most experts don't see South Korea moving into China's camp. But a recent poll by a major South Korean think tank showed that South Koreans ranked China's favorability ahead of Japan's. Beijing is now a larger trading partner for South Korea than Japan and recently agreed to erect a statue of a Korean nationalist who assassinated a senior Japanese official on a visit to Manchuria in 1909 the same man depicted on one of the banners at the South Korea-Japan soccer game.
Biden will make clear on his Asia trip that Washington wants its allies to resolve their differences, U.S. officials say. But experts wonder what he can realistically do.
"There has been a sense that the U.S. should just grab these two countries by their necks and bang their heads together to get them to work together," said Terence Roehrig, a Korea expert at the U.S. Naval War College. "That's not as easily done as folks say."
While the horrors of Japan's 35-year colonization of the Korean Peninsula, which ended only with its World War II defeat in 1945, are ancient history for many Japanese and Americans, the memories remain fresh in South Korea, whose people were forced to work in military brothels and Japanese mines and factories.
South Koreans' feelings are shaped by a perception that Tokyo has never adequately addressed this history. Asia's fourth-biggest economy and a growing diplomatic power, South Korea is also now less willing to heed U.S. pressure and set aside its demands.
Protesters here regularly call for compensation for Korean women forced into wartime sex slavery by the Japanese military and blast Tokyo's claim to South Korean-occupied islets in the sea between the countries.
"The South is now a successful modern society that has surpassed Japan in some areas. But this traumatic and humiliating past still casts a long shadow," Robert Dujarric, an Asia specialist at Temple University's Tokyo campus, wrote recently.
In Japan, public opinion surveys show plunging support for South Korea in the past two years. Popular South Korean stars have all but disappeared from Japanese commercials, and TV stations have cut back on Korean programming, in part because they were deluged with protests when the shows were broadcast.
Protests, while still mostly a fringe movement, have increased this year against Japan's 500,000-strong ethnic Korean population many third- or fourth-generation descendants of those who came or were brought to Japan as laborers during the colonial era.
"It's been a long time since the end of the war and we shouldn't have to keep apologizing forever," said Miki Sakuma, a 44-year-old dental assistant watching an anti-Korean rally earlier this year in Kawasaki.
In Seoul, there's widespread resentment but also some recognition that right-wingers don't speak for all Japanese.
Oh Kyungjin, a 29-year-old associate researcher on international development issues, wants Tokyo to take responsibility for the past but says South Korea can learn from Japan economically and culturally.
"The way the media here talk about Japan sometimes makes me feel that the issue has more to do with getting people's attention by making Japan a public enemy than by showing why Japan needs to apologize," Oh said.
Anti-Japanese voter sentiment weighs on all South Korean presidents, but particularly on Park, whose father is a former South Korean dictator who was close to Japan. She has refused to meet Abe until Japan makes more amends for its colonization of Korea.
The countries' leaders, both of whom are strong-willed and mindful of conservative support at home, would have to make hard political sacrifices to reconcile. Many believe that because of anger in South Korea, Tokyo would have to take the lead.
Compromise, however, currently looks unlikely.
Abe's deputy prime minister, Taro Aso, visited Yasukuni Shrine reviled by South Koreans and Chinese because it honors convicted war criminals not long after representing Japan at Park's inauguration in February.
In April, Abe made remarks that suggested he wanted to revise an official 1995 apology to victims of Japan's wartime aggression. Although he has since backtracked, the damage in Seoul was done.
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Moritsugu reported from Tokyo. Associated Press writers Eun-Young Jeong and Hyung-jin Kim in Seoul, Mari Yamaguchi in Tokyo and Josh Lederman and Matthew Pennington in Washington, D.C., contributed to this report
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Follow Foster Klug on Twitter at twitter.APKlug
