Labelled as an "icon of the alt-metal world", Osborne has been named a key influence by guitarists such as Kurt Cobain (Nirvana), Adam Jones (Tool), Dave Grohl (Foo Fighters), Kim Thayil (Soundgarden), Brent Hinds and Bill Kelliher (Mastodon), Matt Pike (Sleep), Greg Anderson and Stephen O'Malley (Sunn O), Jimmy Bower (Eyehategod), Hank Williams III and Nate Garrett (Spirit Adrift). Adam Jones said that Osborne possesses the two most important qualities for any guitarist, i.e. "attitude and discipline", and compared his artistry with King Crimson founder Robert Fripp. Jones added: "Where I do more of a shoe-gazer thing onstage, Buzz will microwave a crowd." Scott Kelly of Neurosis stated that Osborne's non-cyclical approach to riffs was a massive influence on his band, wherein he plays a section once or at most twice in a song without repeating it again.