They appear not to be as good as they think they are.
Although both former world champions sent out attacking line-ups seeking early points against lowly rivals, both emerged with unimaginative, plodding draws against Bolivia and Venezuela respectively.
Given that both rivals are ranked well outside the top 50 in FIFA's ranking, the stalemates have prompted much head-scratching.
But slow starts by the big guns are something of a speciality in tournament play.
For years, Italy turned the tortoise versus hare approach into something of an art form, particularly at the 1982 World Cup, where they drew all three group matches before suddenly catching fire against Brazil and Germany.
Argentina themselves produced painfully poor early form at the 1990 World Cup—notably losing their curtain-raiser against Cameroon—before going on to reach the final.
With even the two best third-placed teams from the three groups qualifying for the quarters in this Copa America, the chances of either South American giant not making it are infinitesimal.
Hence neither Argentina coach Sergio Batista nor Brazil counterpart Mano Menezes are unduly concerned. At least, not yet.
"In principle there won't be major changes against Colombia," Batista tweeted late on Sunday, as he looked forward to Wednesday's encounter at Santa Fe. "We are very focused on the Colombia match."
Yet Argentina must show what they are made of after allowing Bolivia to strangle most of the life out of Friday's 1-1 draw in La Plata.
That draw, coupled with Colombia edging Costa Rica 1-0, means it is the cafeteros who can go into the game with much of the pressure off.
Brickbats have rained down on Batista and the team since the Bolivia match—fans in the capital were already in a sombre mood following the first ever relegation of 33-time domestic champions River Plate.
Yet the man who replaced Diego Maradona as coach last summer is playing a cool hand.
He has the luxury of deciding if Friday goalscorer Sergio Aguero should start in place of fan favourite Carlos Tevez and has been able to delegate, unwittingly or not, criticism of the team to others.
Witness Argentine Football Association (AFA) president Julio Grondona praising Lionel Messi but slamming the others on Sunday.
Grondona told Radio Del Plata: "Messi always plays well, never badly—which is what the others around him were doing."
One change is in the offing, however, with veteran defender Javier Zanetti, likely to switch to the left with Pablo Zabaleta set to replace Marcos Rojo on the other flank.
Argentina were training later on Monday just outside the capital ahead of a midday flight on Tuesday to Santa Fe.
Brazil, meanwhile, must raise their game against Paraguay in Cordoba on Saturday.
After the 0-0 draw with Venezuela, coach Menezes had to stomach some poor reviews but the Brazilians, going for a hat-trick of titles, have the advantage over Argentina in that in their group everything is all square after Paraguay failed to beat Ecuador.
In any event, despite their early travails, Batista and Menezes will be well aware of who won the fabled encounter between the tortoise and the hare.