At stake is not only the exalted position at the top of the charts, but the bragging rights to being crowned America's finest actor-director, a title both men feel is rightfully theirs.
In one corner is Redford's epic love story, The Horse Whisperer, based on the best-selling novel by Nicholas Evans, and co-starring Kristin Scott- Thomas. Beatty is pinning his hopes on Bulworth, a political farce about a US senator who falls for, and becomes influenced by, a black girl from the ghetto, played by Halle Berry.
Both films opened in America last weekend, Redford's nationwide, taking $14m on 2,000 screens while Beatty's opened only in the big cities, taking $2m on only 12 screens. Though critical reception for both was good, Beatty's is seen as the commercially more dodgy position, with its edgy, outrageous feel.
Though Redford's film is based on known material, he wields immense power on his movies and wouldn't allow score cards to be given out at test screenings. He pulled himself away from his Utah mountain retreat to come to Hollywood and publicise The Horse Whisperer, which has been the subject of much speculation about spiralling costs and the physical condition of its leading man. Asked if he was worried by the competition, Redford, with a glint in his famous blue eyes, replied, "What's there to worry about? My movie is in a class of its own."
Beatty has been an elusive creature in recent years, who has made a way of life out of promising more than he delivers. As he approaches his 62nd birthday, he is also a celebrity being forced into some unfamiliar territory. He is now a husband and father, not a lover-at-large. And his wife, Annette Bening, is out-shining him in the star stakes. Most daunting, as the failure of Love Affair demonstrated, his days as a romantic leading man are numbered. Redford, who is 60, still manages to play the heartthrob in movies such as Indecent Proposal.
Beatty's friends are accustomed to hearing him put down virtually every Redford project, saying, "I read that script and turned it down". Indeed, the quickest way to turn off Beatty is to let it slip that Redford has seen the script first. Beatty was offered projects like Butch Cassidy and Indecent Proposal before Redford, but misjudged their potential. Redford's deal from Indecent Proposal earned him millions.
Only four of the 20 movies Beatty starred in over the course of 35 years could be described as hits, and only two of these (Shampoo and Bonnie and Clyde) were blockbusters. By contrast, eight of Redford's 28 movies were major hits, and several others (The Candidate, Downhill Racer) more than earned back their slender budgets.
With the release of The Horse Whisperer and Bulworth, each has now directed five films, and again one has to tip one's hat to Redford. So far, all of his stints behind the camera were memorable in some way - Ordinary People, The Milagro Beanfield War, A River Runs Through It and Quiz Show - though only his Academy Award directed effort, Ordinary People, fulfilled box-office expectations. Beatty's efforts, meanwhile, have proved a mixed bag. Heaven Can Wait was respectable but forgettable; Dick Tracy was a triumph of style over content; Love Affair was clearly a disaster. Only Reds from 1981 stands out as a significant contribution to his craft.
Redford has taken on a mythic aura among an entire generation of young film makers as the founding father of the Sundance Film Festival, which every year draws a flock of scruffy directors aiming to be the next Quentin Tarantino or Ed Burns. He uses his clout to campaign on eco issues, land rights and the preservation and restoration of national parks.
With all this activity, Redford is, nonetheless, the sort of person who can take a stroll on a sunny day and not cast a shadow. No one quite knows where he lives, or with whom, or how he spends his spare time. Now and then, he does interviews to promote his movies or causes, but he is usually hours late without explanation, and immediately upon hearing the questions, he assumes a rueful expression, suggesting he's sorry he agreed to show up in the first place. "Hollywood is full of people who say they know Warren Beatty, but no one really knows him," says Disney studio chief Joe Roth. "You find very few people who even lay claim to knowing Redford."
As one director puts it, "Redford is the most Presbyterian superstar in the history of Hollywood". Needless to say, Beatty is much more fun, but far more complex. "He procrastinates over everything. Even ordering a cup of coffee becomes an ordeal," reveals a long- time friend. "Every word that comes out of his mouth seems to be inspected, picked over and held up to a light before he parts with it." It is said by those in the know that, during moments of sexual congress, Beatty still chooses his words (and sounds) with the probity of a judge passing sentence.
What both men have in common is a fanatical attention to detail and an awareness of their star power and stature within Hollywood. When Redford notified Disney of his desire to direct The Horse Whisperer, the studio promptly forked out $3m to buy the Nicholas Evans book on the basis of just 30 pages. "It was an extraordinary deal," confirms Disney chief Joe Roth. "But Robert has such a fantastic track record that when he takes responsibility, you trust him."
Disney trusted him to the tune of $20 million to direct and star in the movie, as well as giving him complete control on crew and casting. When the production was delayed by script changes - Redford changed the ending so his character lives - Disney didn't bat an eyelid to the fact that, along with weather delays, the production had rocketed nearly $25 million over its $60 million budget.
More remarkable, perhaps, is Beatty's deal for Bulworth. He turned the conventional process of making movies on its head. "I made the deal before I did the script so I wouldn't have to deal with what was acceptable to the studio," Beatty revealed. "As long as I fulfilled my end, sticking to a slim plot and a $32m budget, I had the simple freedom to make the movie."
Lately, he's been banging heads with Fox over the film's marketing campaign. Many industry analysts predicted Fox would pull Bulworth from its May 15 spot in order to avoid going head-to-head with The Horse Whisperer, but friends say Beatty relished the challenge.
"Warren will be out at theatres gauging reaction and checking to see who has the longer lines, him or Redford," says one.