Greene was known for his unique style of fiddling, which was characterized by its use of double shuffles and syncopation. He was also known for his extensive repertoire of tunes, which included both traditional fiddle tunes and original compositions.
Greene's music has been influential in the development of old-time fiddling. He has been cited as an influence by many other fiddlers, including Bob Wills and Bill Monroe. His music has also been featured in several movies and television shows.