is this the greatest live band of all time?

Roger Waters The Wall, United Center, Chicago
Yes the Relayer Tour 1976
The Grateful Dead, Hearst Greek Theater, Berkley, 3 shows. Gerry was still with it.
Peter Gabriel, Universal Amphitheater, LA 1982
Emerson, Lake, and Palmer, McNichols Arena, Denver. The Works Tour 
Man I could go on...Smashing Pumpkins Hawkwind, Zappa  Too old. Concerts are a young man's game. And they are so expensive! Saw Allman Brothers for $8, Jethro Tull for $10

The Grateful Dead.

This is like asking what is the best painting ever.....very subjective.
That said, there are many good choices in this thread and I would have a hard time arguing against The Grateful Dead.  The Who (1975) may have been the best concert I have seen, although Johnny Cash was memorable too.  So many good ones - I appreciate the artists who are energized to deliver their best performances in front of a live audience. 

For me, it's the Allman Brothers, Grateful Dead, and Pink Floyd