Yet for all their differences, the emphasis was ultimately on co-operation as much as confrontation. In contrast to Richard Nixon's summits with Leonid Brezhnev, or Ronald Reagan's meetings with Mikhail Gorbachev, the Helsinki summit lacked three vital ingredients to be a truly gripping spectacle.
First, the Soviet Union's collapse in 1991 and Russia's turn to free- market democracy have transformed the context. No summit these days can be a piece of chilling real-life theatre, pitting against each other two great ideological adversaries with the power to blow up the world several thousand times over.
Secondly, the impression of superpower equality projected by Cold War summits has palpably faded. Russia, for all its size and strength, is not in the same military or economic league as the United States, and Mr Yeltsin's approach in Helsinki was dictated partly by resentment that the US and its allies are exploiting Russia's relative weakness to reconstruct Europe on their terms.
Lastly, despite their disagreements, familiarity has to some extent bred reassurance and lessened the scope for anger.
This was Mr Clinton's 12th meeting with Mr Yeltsin since 1993; and besides, they exchange correspondence and talk on the telephone more often than probably any previous leaders in Washington and Moscow.
The Helsinki summit was therefore quite different from, say, the meeting which John Kennedy held with Nikita Khrushchev in Vienna soon after the young president's inauguration in 1961. Before that summit, Kennedy was consumed with worry that Khrushchev would write him off as a shallow, soft-touch president incapable of defending the free world against the onward march of communism.
Khrushchev did indeed launch major challenges to the US, including the erection of the Berlin Wall and the attempt to deploy missiles in Cuba. But Kennedy's skillful and determined handling of the latter crisis, coupled with his decision to greatly increase US involvement in Vietnam, left Khrushchev in little doubt about Kennedy's commitment to containing communism.
The Helsinki summit, staged in one of the world's most placid capitals, offered Mr Yeltsin little opportunity to engage in the kind of intimidating showmanship that Brezhnev put on for Nixon in Moscow. A lover of fast, luxurious Western cars, Brezhnev once drove his rival at hair-raising speed through the Russian woods, in a manic celebration of the detente era that was to jerk to a halt in the late Seventies.
The most extraordinary summit was perhaps that of October 1986 in Reykjavik, where Mr Reagan, meeting Mr Gorbachev for only the second time, came close to agreeing to the abolition of all the world's nuclear weapons. Margaret Thatcher and other European leaders were horrified by what they saw as Mr Reagan's naive idealism.
Total nuclear disarmament has never been on a summit agenda since. But at Helsinki Mr Clinton and Mr Yeltsin discussed a US proposal to reduce each country's nuclear arsenal to 2,000-2,500 warheads from more than 10,000 in the late Eighties.
While recent US-Russian summits in Moscow and Washington may have lacked passion and urgency, Helsinki was the scene of a crucial encounter in 1990 between Mr Gorbachev and George Bush. This was when the US President sought Moscow's support for a US-led military campaign to drive Saddam Hussein's forces out of Kuwait.