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. 

Dire Straits on the top of my book.

I LOVE the Beatles BUT they're a studio band.

The correct answer is U2.

I love these posts because it helps me size up everyone here!  Saw J. Geils in '72 and a great show!  As a musician, I look at different things than just the energy level.  Virtuosos like ELP and Yes and Tower of Power, stand out for me.  But Earth, Wind & Fire is still fantastic.