Clarke's Australian team leads the five-Test series 2-0 and is hoping to regain the Ashes in Perth. Cook's team has won the past three Ashes series but after going through a year without defeat, has suddenly slumped to back-to-back defeats in this series.
Understandably both players will therefore put more emphasis on their teams, but the coinciding hundreds warrant attention.
The 32-year-old Clarke made his debut in India in 2004, late in Australia's prime period in modern cricket, and has scored 7,940 runs at an average of 52.58
Cook, who will turn 29 later this month, made his debut in India in 2006 and has scored 7,883 runs at an average of 47.20, the kind of return that his deputy believes already puts him on the path to greatness.
"I don't know the records that he is about to break but there are going to be a few of them," England vice-captain Matt Prior said Wednesday. "He will be probably the greatest England cricketer.
"In my mind there is no doubt about that and from a leader point of view there is no other man I'd want leading us on to the field, because he leads from the front and leads by example and I expect he will do exactly that in this game. A massive congrats to him for playing 100 games - incredible."
Australian fast bowler Mitchell Johnson wants to terrorize the England batsmen for the third time in the series to deliver his skipper a fitting 100th Test.
"It's a phenomenal effort to make 100 Tests," Johnson said. "It's a lot of days out in the field and a lot of heartache that goes with it, but also a lot of happy times as well, like we're going through at the moment.
"He'll definitely be feeling a bit. He'll be nervous and I'm sure excited at the same time."
Clarke went through a drought of nine Tests without a win, including a series sweep in India and a 3-0 Ashes defeat in England, before winning the first two Tests of this series. Clarke has been in form with the bat, too, scoring centuries in Brisbane and Adelaide.
"The past 12 months, I've been really happy with his style of captaincy," said Johnson, who has taken 17 wickets in the first two Tests. "He's been aggressive when he needed to be, pulled it back when he's needed to."
Clarke was fined after the 381-run win in Brisbane because an obscenity he used in a heated verbal exchange with England's James Anderson was heard on the TV broadcast. Tension has been high in the series, with Clarke being unusually combative in the field. It's a hard-nosed approach his players are supporting.
"I thought it was great what he did," Johnson said. "He stood up for the players. That's what you want from a captain."