One "warhorse" they never done justice to live is "Start me up", I think. I always prefered the "Tattoo You" studio version.

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skipstone
There are a few others but it really starts to fall off after those few. I really liked how they did Monkey Man on the Licks tour (and even Voodoo tour) but it was essentially a very faithful copy of the LP version except for Lisa's horrible screaming.

Faithful? Are we talking about the same thing here? On Four Flicks, Chuck TOTALLY messes up the piano part of Monkey Man, getting worse as the song progresses.

Come to think of it; almost all the songs on "Tattoo You" have been manhandled live.

I witnessed a version of Midnight Rambler in Hershey on the ABB tour that was by far the best song I ever heard live .

Despite very very good Studio albums set the Stones in remarbable Style and Standard I did and I always will prefer seeing them or others live on stage.
Only during a live appearance you smell and feel the vibes of a good or a bad evening, of a lesser or better audience. Sometimes the air seems to explode in thunder and lightning sometimes there just emptyness thought they try very hard. Even if they play bad and worse you will never capture such in a studio except if they play and record the tunes in one go, like they did some songs in Tattoo you.