They deliver in different ways, with one creating great cinematic spectacle and the other performing quite a number on our emotions.
Anderson, who made his name with Boogie Nights, is probably the most distinctive of the pair, his style becoming weightier, more intensely cinematic, with each film. He follows his magnificent There Will Be Blood with a film that is equally well-acted and enigmatic, though falls short of the other's perfection.
The Master opens at the end of the Second World War, with troubled naval officer Freddie Quell (Joaquin Phoenix) struggling to readjust to civilian life. Having tried his hand as a store photographer, then as a field hand, where one of his alcoholic concoctions (he is quite the alchemist with the booze) almost kills someone, Freddie finds his way onto a ship that is commanded by Lancaster Dodd, aka The Master (Philip Seymour Hoffman).
Dodd introduces himself as a writer, doctor, nuclear physicist and philosopher, adding: "but most of all, I'm a man." He's also the charismatic leader of The Cause, a new movement that seeks to offer a path to aimless post-war souls and is clearly akin to Dianetics, L Ron Hubbard's precursor to Scientology.
Anderson's interest is not in chronicling Hubbard's crazy legacy (which feels like a missed opportunity, actually), but in the bond that forms between the alcoholic Freddie and the older man, who sees him as a protege. In the pair's first scene together, Dodd carries out an "informal processing" of his stowaway (what Hubbard called "auditing"), an intense questioning intended to extract Freddie's most painful memories. It's simply astonishing, crackling with tension, angst and personality, and is perhaps the best two-hander you'll see all year.
It's impossible to take your eyes off Phoenix throughout the film. His face is like granite, his mouth clenched in contemptuous challenge. The main challenge offered by the film is to work out what makes this ferocious, frightening loner tick. Its failure, however, is that, in contrast to Freddie, the Master is eventually revealed as no more than a showman, an empty rhetorician, making The Cause up as he goes along; as his movement drifts along, so eventually does the story.
But as a cinematic spectacle and a study of an extremely original character, it's highly distinctive. Shooting with the 65mm film stock that was popular in the 1950s, Anderson creates one thrilling, crisply beautiful image after another, accompanied by Jonny Greenwood's jazz-infused, typically unusual score.
Rust & Bone is a love story whose premise ought to be preposterous. It's testament to Audiard's skill as a director that he makes it profound.
He's helped mightily by the fact that his star is Marion Cotillard, who one feels can do anything she likes on screen. She's heartbreaking as Stephanie, the marine park trainer whose life seems over after a terrible accident but is somehow coaxed back to life, and back into bed, by Ali (Matthias Schoenaerts), a taciturn man whose complete lack of sentiment is the key to his success both as an illegal street fighter and as an informal carer.
It's a rich mix, of the kind in which Audiard specialises; after all, The Beat That My Heart Skipped was a crime drama whose central character yearned to be a concert pianist. As with that film, and A Prophet, the director combines melodrama and verite in a way that is gripping and extremely moving.