is this the greatest live band of all time?

What a "loaded" question!
So subjective. Best recorded live show - Allman Brothers @ Fillmore East.

At the show: Grateful Dead when touring with that insane equipment known as the Wall of Sound. Look it up, mostly McIntosh amps.
Sting at The Bottom Line w/original Dreams of the Blue Turtles band.
Steely Dan at Red Rocks

Floyd was excellent, but stuck to the script, same goes for the Stones.

Too many more to list. 

@ dweller
Agree 100% when talking about Floyd, saw both DSOM and Wall and both were excellent, sonics were phenomenal.  The only concert sound I've heard that I thought was better was Sting.  Captured very well on the "Bring on the Night" CD.  I saw that tour at Radio City Music Hall sometime in '85.

Don't like just noodling around aimlessly from a band.

But, I can and have listened to the Allman Brothers jam their a$$es off.