As a rivalry, it is unrivalled in both longevity and consistency. Arsene Wenger has 15 consecutive top-four finishes and, in the history of English football, only one manager has more. Needless to say, he is Sir Alex Ferguson. Yet as the Scot has been ejected from the Champions League and the Frenchman faces his own exit, for the first time in a generation the Arsenal manager may be denied an invitation to next season's competition. It all prompts a question: how and where do epic careers end?
A growing band think that Wenger's time is up. 'Fergie time', that elastic period towards the end of a game where Manchester United achieve ever more, may have begun in 2002 when their manager rescinded his retirement. The one man not gazing at his watch, it seems, is the 71-year-old himself, insisting his health alone will determine his departure. He is not counting down the days. Yet after United kept chief executive David Gill's forthcoming move a secret, it could be another Ferguson smokescreen. Or maybe not.
Earlier in the season, many around Old Trafford thought it would be Ferguson's final year. Now the majority believe he will continue. In doing so, he could win still more or deprive himself of a happy ending. Ferguson's achievements are so enormous that he cannot tarnish his legacy but a serial winner has already ignored opportunities to walk away on a high.
Two such offered a particularly compelling conclusion to his career: 2008, when he had made United European champions again, capping his own comeback from the awful autumn of 2005, and 2011, when he secured their 19th title and, decisively, knocked Liverpool off their perch. One who knows Ferguson better than most suggests he genuinely is not concerned about going out on top, but it would be out of character for him to take his leave in a year when, say, Manchester City won the league.
Wenger may not have the same luxury of choice. Arsenal will not sack him but there is an increasing feeling that his current contract, which expires in 2014, is his last and that the strain is finally telling. His, and Arsenal's, decline is exaggerated. Despite the eight-year trophy drought, from 2001 to 2010, he had a side that was invariably among the best six in Europe. The problem was that, for the second half of that time, two or three of the other elite half-dozen were also English.
Now success is stability; even were Arsenal to finish in the top four and lift silverware next season, the reality is that they are further from winning the league than at any point in his reign. Eight years younger than Ferguson and previously coveted by Real Madrid, Barcelona and Paris Saint-Germain, he may not be finished. Yet his options may be limited. His vocal opposition to "financial doping" and enduring idealism may rule out the lucrative globe-trotting that cushions the path to retirement for contemporaries such as Guus Hiddink, Fabio Capello and Sven-Goran Eriksson. The hedonistic Swede may be fulfilled by it, but the austere Italian probably isn't.
For the finest managers, there are warnings from the present and unfortunate precedents from the past. It rarely ends well. Ferguson has long been aware of the parallels with Sir Matt Busby yet nevertheless hinted that, like his illustrious predecessor, he could become a director. It opens the way for his successor to become a second Wilf McGuinness and for Ferguson, like Busby, to make a messy return to the dugout.
Wenger's eventual fate is to be immortalised in a statue outside the Emirates Stadium alongside the man he displaced as Arsenal's greatest manager, Herbert Chapman. The revolutionary from the 1920s and the 1930s died in situ. So - as his assistant and replacement Ferguson knows from harrowing experience - did Jock Stein, who passed away shortly after Scotland's 1-1 draw with Wales in 1985. Valery Lobanovsky, Hennes Weisweiler and Ernst Happel were others to die in the dugout; not literally, but in each case football was their life.
For many, it is an existence of diminishing returns. Plenty - Jose Villalonga, Miguel Munoz, Alf Ramsey, Stan Cullis and, perhaps, Rafa Benitez - have their finest moments at a comparatively young age. Modernisers like Arrigo Sacchi, Helenio Herrera and Nereo Rocco became outdated, ending without a trophy in years. Don Revie was a pariah in exile. His arch-enemy, Brian Clough, was a blotchy-faced figure who saw relegation through an alcoholic fog in his final year; Otto Rehhagel, too, ended with the ignominy of demotion. Carlos Alberto Parreira bowed out with the failure of South Africa's World Cup campaign. Hiddink's international career was curtailed when the great overachiever failed to even quality for consecutive tournaments.
No matter how many managers claim they are better at their job than they were 10 years earlier, few improve after their 60th birthday. Yet management is a drug and they are compelled to feed their addiction.
Sir Bobby Robson was desperate for any job long into his 70s. His protégé, and the president of Ferguson's fan club, Jose Mourinho, has said he hopes that, like the Scot, he is still managing at 71. Yet look at those who are: Leo Beenhakker has taken ever more obscure jobs. Giovanni Trapattoni has become a divisive figure in Ireland, involved in rows with players such as Stephen Kelly and Kevin Foley, men who would have got nowhere near his magnificent Juventus teams. The lack of respect for a legend is sad.
Yet Trapattoni, like many others, is trying to recapture the magic of earlier days. Few do. Rinus Michels, a rival of Ferguson's for the title of football's finest manager, even if his importance is measured more in influence than major honours, won the 1988 European Championship with Netherlands and had arguably the most accomplished side in the 1992 tournament. But missing penalties is as much of a tradition as Total Football in the Dutch game.
Few go out with the gleam of silverware. Bill Shankly did, surprising all by choosing to leave Anfield after winning the FA Cup in 1974. Yet having stage-managed his retreat from the front line, he came to regret it. Liverpool's most iconic manager became Everton's most famous spectator in an unrewarding retirement. For him, like many another, management was his passion.
So in the search for a manager who bowed out happily and at the height of his powers, there may only be one man to tick all the boxes. Shankly's successor Bob Paisley left, having won his sixth league title and his third League Cup, in 1983. He retains the distinction of being the only manager to win the European Cup three times. Yet he was the exception in many ways. Never his own boss until he was 55, Paisley was the reluctant manager. The same cannot be said for those ageing obsessives, Ferguson and Wenger.