Good one, @iloveromy! I saw both versions, with Cooder in the Little Village group (with Nick Lowe and Jim Keltner) on a sound stage in Burbank, the version with Landreth at The Roxy Theater on Sunset Blvd. in Hollywood.
The above and the following are impossible to rate as absolute "best", but all great:
The Dave Edmunds Band at a big club in NYC (the name of which I don’t recall) in 1982. 100% high-octane rocket fuel Rock ’n’ Roll!
Not far behind, NRBQ at The Roxy Theater in Hollywood, a couple of times. The most "fun" live band I’ve ever seen.
Marshall Crenshaw at The Peppermint Lounge in NYC, 1982. Graham Maby (from Joe Jackson’s band) on Fender 6-string bass, 4-part harmonies!
Rockpile at The Country Club in Reseda, CA, 1980. All American Rock ’n’ Roll at it’s finest, ironic considering all the members are from the UK.
The Band at The Berkeley Community Theater, 1969. The finest live music making I’ve ever heard, on the level of a Jazz band.
The Beat (U.S., not U.K.) at The Whiskey, the best Power Pop band I saw and heard live, including The Who.
The Electric Flag at The Santa Clara County Folk-Rock Festival in 1968. Mike Bloomfield on guitar, the mighty Buddy Miles on drums (who made Keith Moon look like a wimp ;-), four saxes---two baritone, two bass!
For singer/songwriters, the sublime Iris Dement, at The Troubadour in Santa Monica and The Aladdin Theater in Portland, OR. I want her music played at my funeral. ;-)
Leonard Cohen’s live show was the "grandest" I’ve ever seen, pure class.
By the way @allexandar, I saw The Beatles at The Cow Palace (S. San Francisco) in ’65, and they weren’t very good live. Honest! Better than The Stones, though, who absolutely reeked. The most over-rated band in the entire history of Rock ’n’ Roll!