One has ordered his forces into battle more times than any other postwar British leader. The other threatens military action against "evil" nations and keeps a scorecard of dead al-Qaida leaders, marking each fatality with an X.
Now, Tony Blair and George Bush have received international recognition for their unswerving willingness to use force: a nomination for the 2002 Nobel peace prize.
The prime minister and US president have been jointly nominated for the accolade by a rightwing Norwegian politician who believes their military campaign against terrorism meets Alfred Nobel's criteria that the winner "shall have done the most or the best work for fraternity between nations, for the abolition or reduction of standing armies and for the holding and promotion of peace congresses".
Harald Tom Nesvik, who represents the Party of Progress in the Norwegian parliament, said yesterday: "The background for my nomination is their decisive action against terrorism, something I believe in the future will be the greatest threat to peace. Unfortunately, sometimes you have to use force to secure peace."
Mr Nesvik has nomination rights as a member of a national legislature.
The committee keeps the names of nominees secret for 50 years, but those making nominations often make their choice public. The full list of nominees will not be completed until later this month.
There are signs that Mr Blair and Mr Bush are up against tough competition to secure the $940,000 (£670,000) prize money and see their names added to an elite list which includes Martin Luther King, Mother Teresa and Nelson Mandela.
Other unconfirmed September 11-related nominations are believed to include Rudolph Giuliani, the former mayor of New York, and Guy Tozzoli, an engineer who helped design the World Trade Centre.
The winner will be announced in October.
Mr Blair's nomination appears to have brought little cheer to Downing Street. Last night a No 10 spokeswoman said: "I think it would be a matter for the committee to consider any nomination. I don't think it would be a matter we would comment on."