 By Your Side was generally well received by critics. Regarding the songwriting, most reviewers praised The Black Crowes for returning to the straightforwardness of Shake Your Money Maker (1990) following the more adventuresome Amorica (1994) and Three Snakes and One Charm. Gemma Tarlach of The Milwaukee Journal Sentinel welcomed the album "because it represents a great band's return to what it does best", calling it "45 minutes of good, dirty fun". Wall of Sound's Russell Hall found that the band's emergence from "the jam-band haze that's infected" their recent work resulted in a "laser-sharp focus". Mark Falkner of The Florida Times-Union said that beyond the band's mastery of their influences' musical styles, what prevents them "from being just another tribute act is that they have (also) mastered the power, the passion and the fun that made the mix work". Some critics, also noting the change in approach, derided the band for returning to mine the same influences perceived in their debut album. Jim Farber of the Daily News thus described By Your Side as "a copy-of-a-copy-of-a-copy" and marked "Go Faster" a sped-up version of Humble Pie's "Hot' n 'Nasty". The Times' Nigel Williamson called "HorseHead" "Zeppelinesque" and labeled "By Your Side" "a kicking boogie half way between [the Faces']' Cindy Incidentally 'and [The Rolling Stones'] 'Tumbling Dice'". Steve Dougherty of People summed up by commenting, "Purists will wonder why to buy this album when [The Rolling Stones'] 1972 Exile on Main Street or [Rod] Stewart's 1970 Gasoline Alley exist on CD."
