The version on the If God Will Send His Angels single was Bono and the Edge live in the studio (with some accompaniment, obviously), which was beamed via satellite to Sinatra for his 80th birthday.
The song was written for him (also obviously), but he died before he could record it. His daughter, Nancy, recorded it for the eponymous album she released last year (and Adam and Larry played on it with her; so I guess if you combine those two recordings somehow, you'd have a full band recording, heh).