The debate rages on over whether a Netflix movie is legitimate, bona fide cinema, as the streaming behemoth has somewhat reluctantly joined Amazon Studios in giving its award-hungry offerings at least a limited theatrical run. But good old-fashioned talent makes contrasting the streamers with their Old Hollywood rivals a moot point. And, along with star-studded casts and esteemed directors, many of this season’s Netflix and Amazon original films were soundtracked by prestige composers.

“Roma” had no original music, but Netflix scored a coup with “The Other Side of the Wind,” the belatedly released Orson Welles film that features a new score by three-time Oscar winner Michel Legrand. Meanwhile, Amazon nabbed not one but two Radiohead members for its original features this year: Jonny Greenwood for “You Were Never Really Here” and Thom Yorke for “Suspiria.”

Netflix’s “The Ballad of Buster Scruggs” is the latest in a 35-year collaboration between the Coen brothers and composer Carter Burwell, who’s proved equally deft at italicizing their quirky humor and darkening their cold drama. He needed to walk the razor’s edge between both in the Coens’ western anthology, which has Tim Blake Nelson grinning and singing over his kill in one chapter, and then a stoic Liam Neeson carting an armless, legless thespian (Harry Melling) around in a very bleak story that follows.

Burwell’s score — which ambles from a rustic hymn for acoustic guitar and strings, to a wintry dirge, to a sentimental flute lullaby, to an ink-black rumination on death — is almost like a miniature songbook of his career. He first tried tying all of the disparate chapters together with a unifying theme, but quickly realized that didn’t work. Instead, he embraced the film’s episodic nature and the unity simply became — himself.

“In the end, it’s a Coen brothers film and it’s a Carter Burwell score,” he says. “So we pulled it back to just sounding more like us.”

Another longtime partnership, between director Gus Van Sant and composer Danny Elfman, dates back to 1995’s “To Die For.” Two of the composer’s four Academy Award nominations were for Van Sant films: “Good Will Hunting” and “Milk.”

In the director’s dramedy for Amazon Studios, “Don’t Worry, He Won’t Get Far on Foot,” Joaquin Phoenix plays Portland cartoonist John Callahan, who overcame the alcoholism that led to a car crash, which rendered him a quadriplegic. Elfman’s score begins with the farthest thing you’d expect from the composer: free-form jazz.

“Anytime I can do anything where someone says, ‘That couldn’t be from you,’ that’s like my highest compliment,” Elfman says.

The rest of the score was written for a tiny ensemble of seven players. There are some wordless vocals, but most of it is just a guitarist and Elfman on keyboards and synths. That was mainly due to the film’s small budget, but Elfman enjoys taking a break from the symphonic juggernauts — including his recent score for “The Grinch” — and stripping things down.

“It’s a chance for me to be more personally engaged, not with the writing, but with the performance of the score,” he says.

He and Van Sant didn’t have a roadmap for the film’s musical tone or style, only that they wanted to avoid maudlin. Theirs is a process of constant experimentation, throwing wildly different ideas at the picture and seeing what sticks.

“If you were a painter, it would be the difference [between] doing a lot of sketches first before you commit to the painting, because it has to achieve a specific whole entity, [whereas] with Gus, it’s going to be more like doing a Jackson Pollock.”

A less familiar name to American moviegoers, Nitin Sawhney has been scoring films and videogames for 20 years. The Londoner’s background in both Indian and western classical music made him an ideal fit for “Mowgli: Legend of the Jungle,” director Andy Serkis’ dark adaptation of the classic Rudyard Kipling tale of an Indian boy raised in the jungle. Netflix bought it from Warner Bros. and released it in December.

“It’s a hero’s journey, but it’s also a coming-of-age [story],” says the composer, who identified with the young protagonist. “I grew up in an area in England where there’s a great deal of racism, and so I felt quite torn between being, I think, the only Asian in my area, and my home life — and feeling like I was between two worlds.”

Sawhney’s score braids Indian percussion instruments including the mridangam, pakhawaj and tabla into a traditional symphony orchestra. His theme for Mowgli is a bittersweet melody often played on bansuri, a bamboo flute. “I was trying to find something that felt like it had a lot of heart, and captured his innocence, too.”