It's one of the oldest rivalries in sport. The two adversaries have done battle on tennis courts and motor circuits, tussled on the high seas and the ski slopes, and fought it out in stadiums and velodromes.
Now they are contending on the golf course.
From the elegantly manicured pastures of America to rough-hewn links of the British Isles, technology and tradition are vying for preeminence.
And so far, technology has the upper hand.
A series of recent design breakthroughs in both clubs and balls - some of them highly controversial - has enabled golfers to hit farther and farther. Some courses are looking tame, anachronistic even, when exposed to the power of the new giant hitters.
Even the Royal St. George's, where the British Open started Thursday, has added 250 yards to try to hold off the charge. But this venue has another, better equalizer. On the rugged British "links" courses, with their treeless fairways, coastal gusts, and knee-high fescue, nature becomes tradition's ally.
"The UK Open is always one of the toughest tests around because of the courses that are played on," says Stewart McDougall of the Royal and Ancient Golf Club, which governs the game outside the United States and which organizes the British Open. "The courses are different from a lot of the American courses.
"They are designed to make it an overall test of golf that makes you go through the whole armory, not just long driving and not just pitching and putting," he adds from the venue for this year's 132nd British Open championship, near Sandwich, in southeast England.
Nature has certainly been the deciding factor in recent British Opens. The course at Carnoustie in 1999 was so savage, with the narrowest of fairways and the deepest of rough, that it was nicknamed "Car-nasty".
Last year, at Muirfield, some of the roughest weather the tournament has ever seen blew in from the North Sea and blew away the best. Tiger Woods, the world's number one, recorded the worst round of his professional career.
Woods was gracious about the weather that day, but is less so when discussing the issue of advances in technology. A golfing natural with one of the longest drives in the game, Woods has seen his advantage disappear as new designs help the rest of the field catch up.
Lightweight titanium drivers, graphite shafts, and solid-core balls are revolutionizing the sport. Club heads are fatter and broader, with a larger "sweet spot." And in one hugely controversial development, some drivers are purportedly being crafted with "springy" faces that compress when they strike the ball and trampoline back into place as they propel it, greatly increasing the distance the ball travels.
Woods has called for compulsory testing of drivers to ensure that "illegal" clubs aren't being used. But so far, his calls have fallen on deaf ears. And meantime, the distances that players attain from the tee just keep getting longer.
"Trampoline-effect drivers and composite balls have meant that 300-yard-plus drives are becoming the norm not the exception," says Allan Kelly, a golf writer covering the British Open for Agence France-Presse.
"The Royal and Ancient admits that they are basically powerless to prevent illegal equipment and that this week's Open might well be won by a player using an illegal driver," Mr. Kelly adds.
Enter nature. The Royal St George's course typifies the challenge of the capricious British links course: unpredictable fairways undulating over a sandy, almost lunar landscape ominously exposed to North Sea gusts.
The par-71 course is not the longest in the world, but what it lacks in distance it makes up in guile and mystery, so much so that Ian Fleming (a member of the Royal St. George's) used it as the inspiration behind one of the most famous golfing scenes in cinematic history: a confrontation between James Bond and Goldfinger.
British Open organizers have stopped short of deploying international villains and lethal Korean manservants to make the course tougher, but it has made some design changes to keep the big hitters guessing.
New, deep bunkers, blind tee shots, and the most formidable rough all mean that players might be wiser going for position rather than distance.
"Distance isn't going to be the number one thing," Sandy Lyle told reporters. He won the Open on this course 18 years ago. "It's going to be pretty much keep it in play, a lot of irons off the tee."
Last year's champion, South African Ernie Els, agreed. "To hit the fairways here in some places, it's impossible," he told reporters. "If we get bad weather this might be the toughest one of the lot."
It was certainly looking that way as the tournament began Thursday. A week-long heat wave giving way to damp blustery conditions that left many golfers looking as if they'd rather be somewhere else.
One contender, Jerry Kelly, took 11 strokes on the opening hole. Woods finished the first round Thursday with a two-over-par 73, after a rocky start. He let rip with his big drive on the first tee and immediately lost a ball in the tall grass to the right of the fairway. Despite the frantic efforts of players, caddies, officials, and spectators, they failed to locate the ball and Woods suffered the embarrassment of having to return to the tee in a buggy. He recorded a triple-bogey seven on the open hole.
It's unlikely to be the last debacle in the four-day championship if nature and tradition have anything to say about it.
• Material from the wire services was used in this story.