Athletic Bilbao's Marcelo Biesla, in a baggy track suit, wearing glasses with strings attached, is a deep-thinking, philosophical coach who believes the only way to win is to take the game to the opposition whatever the circumstances.
On Wednesday, Simeone's more rugged style came up trumps against his idealistic fellow Argentine and former mentor when Atletico trounced Bilbao 3-0 in the Europa League final.
Bielsa has been lauded for the way he has transformed the previously physical Bilbao into one of Spain's best passing teams, despite being limited by the club's Basque-only policy.
The eccentric Bielsa, who coached Simeone for four years with Argentina, has taken Bilbao to their first European final in 35 years and led them to the Copa del Rey final, where they face Barcelona on May 25, in his first season in charge.
Barca coach Pep Guardiola is among the admirers of Bielsa's style which dictates that his team play a high-tempo passing game and pressure the opposition in their own half.
However, that adventurous approach can also leave his sides badly exposed as Chile fans found out during three heavy losses to Brazil and a 3-0 home defeat by Paraguay under Bielsa's leadership, all in competitive internationals.
The early signs on Wednesday at the National Arena were ominous as Atletico went straight for the jugular and Bilbao gave away possession three times at the back.
After scoring in the seventh minute, the game was exactly how Atletico wanted it as they disrupted Bilbao's usually flowing game with niggly fouls in midfield, while remaining a potent threat in attack.
Bielsa said he may have played into Simeone's hands.
"We wanted to play a certain way but we didn't create the ideal scenario for this, our opponents managed to turn the scenario into one which suited the way in which they aspired to play," he said.
"I feel fundamentally responsible for the distance there was between what we are capable of producing and wheat we actually produced."
Simeone boosted his own coaching career which began with a flourish in his native Argentina but then appeared to be spiralling downwards after a couple of significant failures.
In only his first year as a coach, the former Argentine midfielder, often described as playing with a knife between his teeth, led Estudiantes to their first Argentine championship title in 35 years, making him an instant hit.
He then moved to River Plate and another title followed one year later.
But it all went sour in the following championship as a run of 11 games without a win left River bottom of the table and an angry Simeone, who broke his hand when he smashed it on the substitutes bench in frustration in one game, left the club.
He then took on a huge task as he moved to debt-ridden San Lorenzo, stayed for a year and left amid fan protests following another poor run.
At that moment, he was in danger of joining the journeyman coaches who flit from club to club. But a spell in Italy with Catania, who he saved from relegation, raised his stock.
In December, he took over at Atletico, a club with which he has a strong identity after winning a Liga and Copa del Rey double in 1996.
"It's always marvellous to win as a player, you enjoy it more (when) you are on the pitch. You can shout and run and do the lap of honour. As a coach I have to be more restrained and watch from the sidelines.
"I'm really happy to give the Atletico fans another trophy, this time as a coach," he said, managing a rare smile.
"I am a young coach, this is without doubt a very powerful situation for me, thanks to the affection the fans have for me," he added having restored his managerial reputation.