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 started poorly 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.
Batista on Monday confirmed that he would largely keep faith with the team held by the Bolivians, confirming just one change -- with Manchester City's Pablo Zabaleta to replace Marcos Rojo on the right side of defence while veteran Javier Zanetti switches to the left.
"I don't like to chop and change the team around from one game to the next," Batista told reporters.
"I will stick with the team and we will see how things go."
That means Napoli's Ezequiel Lavezzi completing an attacking trident as Batista keeps faith with both Carlos Tevez and Lionel Messi -- the latter still struggling to find his club form with his country.
But Batista did warn that "there will be some changes for the third game (against Costa Rica) if we play as we did against Bolivia."
His decision to limit changes for now means Sergio Aguero of Atletico Madrid, who volleyed in a superb equaliser against Bolivia, will again start on the bench.
Batista praised Lavezzi and Tevez for bringing both speed and possession to the table.
"Carlos can link up with Lionel, (bringing) not so much speed but keeping the ball," he said.
Argentina have to rebound after the Bolivians deservedly held them to a 1-1 draw in La Plata last Friday.
With Colombia edging Costa Rica 1-0, it is the cafeteros who can go into Wednesday's game with much of the pressure off.
Many Argentine fans are unconvinced that Tevez and Messi are the men to unlock the door in attack, yet dropping either would be open up a hornets' nest.
Although Messi is struggling somewhat to fit into the system, he has the support of powerful Argentine Football Association (AFA) president Julio Grondona, who insisted on Sunday that "Messi always plays well, never badly -- which is what the others around him were doing".
Argentina trained on Monday at Ezeiza, south of 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 their dire 0-0 draw with Venezuela.
Yet, despite their early travails, Batista and Menezes will be well aware of who won the fabled encounter between the tortoise and the hare.
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