There is no shortage of support for the view that it makes little difference who wears the armband in a football team. You can give the captaincy to the best player (Cesc Fábregas), or the most famous (David Beckham), and the team's performance will still be defined by its members' individual and collective merits and the quality of coaching they are given. From that perpective, it matters little whether or not Fabio Capello chooses to reverse his decision to dethrone John Terry in time for next week's Euro 2012 qualifying match in Cardiff.

History offers a contradictory view, in the shape of the keen intelligence of Danny Blanchflower and Franz Beckenbauer, the calm authority of Bobby Moore and Franco Baresi, or the controlling industry of Billy Bremner and Didier Deschamps. And, as it happens, a great deal of opposing evidence comes from the two clubs sitting at the top of the Premier League, where Manchester United and Arsenal offer contrasting lessons in leadership.

Sir Alex Ferguson has always looked for players with a significant influence on the pitch and in the dressing room. His big three captains have been Bryan Robson, Roy Keane and Gary Neville, with interludes from Steve Bruce, Eric Cantona, Rio Ferdinand and Ryan Giggs. The present incumbent is Nemanja Vidic. These players personify strength, resilience, and a certain kind of footballing integrity in sufficient quantity to overcome individual defects, such as Robson's drinking or Cantona's quixotic nature. Even in their less exalted periods, rarely have Manchester United looked bereft of leadership on the field of play.

The role seems to mean something very different to Arsène Wenger. Just as Ferguson inherited Robson, so the Frenchman found Tony Adams, who would become the only man to captain a title-winning side in three different decades, already in place. After Adams's retirement in 2002 he could promote his deputy, Patrick Vieira, another powerful character who did not embody the Arsenal ethic to quite the same degree but nevertheless inspired awe among his team-mates and could change a game almost single-handedly.

Vieira led the team through the unbeaten season of 2003-04 but lost form the following season and was sold to Juventus in the summer of 2005. At that point the Arsenal armband was given to Thierry Henry, the club's best player and leading goalscorer, who was thought to be in danger of accepting an offer to move elsewhere. Henry stayed two more years, during which Arsenal failed to regain the title and lost to Barcelona in a European Cup final on which the French striker's influence was nonexistent.

In captaincy terms, he had fallen far below the standard set by Adams and Vieira (or, in previous generations, Joe Mercer and Frank McLintock). Nor was his successor, William Gallas, another player coveted elsewhere, much more effective. The French defender, given the job ahead of Gilberto Silva, Henry's quietly effective deputy, held the job for only a season and a bit, his tenure most notable for his bizarre sit-down protest at St Andrew's in 2008, the match in which Eduardo da Silva's leg was broken by Martin Taylor's challenge.

Gallas lost the position 14 games into the 2008-09 season, when Fábregas was appointed. Although only 21, the Catalan was clearly the club's outstanding performer. But given that there were already rumours linking him to a return to Barcelona, it was impossible to escape the thought that Wenger had once again given the armband to a player he wanted to flatter into staying.

Like Henry and Gallas, Fábregas has not been an effective captain. Injuries have limited his appearances, and he has sometimes tried to return from them too soon. But there are many who believe that, rather than putting all his faith in youth, Wenger would have done better to rely on the experience of Silva for a couple of seasons before identifying a younger player with the necessary attributes.

Wenger is a great football man and an outstanding contributor to the history of the English game, but he has some curious quirks and blind spots. Putting the No10 on the shirt of a centre-back (Gallas) and the 3 on a right-back (Bacary Sagna) represents one of them. Failing to appreciate – or perhaps to accept – the influence of a good captain on a team's mentality is another, and it is the one for which Arsenal are currently paying a heavy price.