This is an unusual situation when talking about covers. “Woodstock” is a song which is hard to determine which is the original version. Joni Mitchell wrote it for Crosby, Stills, Nash & Young, who recorded it for their 1970 album “Deja Vu”, but Mitchell also recorded the song in several other versions around that time and later, starting with her 1970 album “Ladies of the Canyon.” She wrote the song about the experience she never experienced herself. She was invited to attend and possibly play on the legendary festival, but her management thought it was more important to be a guest on the Dick Cavett Show. She wrote it in a hotel room in New York City, watching televised reports of the festival. "The deprivation of not being able to go provided me with an intense angle on Woodstock," she told a journalist several days after the event. Anyway, Mitchell managed to write one of her most beautiful songs in her highly creative career, based on the stories told by Graham Nash, who was her boyfriend then. She also managed to give the song several incarnations in different genres and moods. All of therm are beautiful, including that of Crosby, Stills, Nash & Young.
Prior to release on any album, Mitchell performed "Woodstock" at the 1969 Big Sur Folk Festival, one month after Woodstock. Released on Mitchell's third album Ladies of the Canyon in March 1970, "Woodstock" served as B-side for that album's single "Big Yellow Taxi". Mitchell re-recorded "Woodstock" for her two live albums, “Miles of Aisles” and “Shadows and Light.” Crosby, Stills, Nash & Young's upbeat hard rock arrangement was released as the lead single from their 1970 “Déjà Vu” album, with a rock arrangement and slightly altered lyrics. The Crosby, Stills, Nash & Young version of "Woodstock" peaked at number 11 on the Billboard Hot 100 in May 1970 and number 3 in Canada. "Woodstock" became an international hit in 1970–71 via a version by the band Matthews Southern Comfort, which resembles the Joni Mitchell original. My favorite is Joni’s version from a live in-studio TV performance that happened in London in 1970, and you can choose yours, of course.