electro-harmonix Memory Man used to be Edge's orignal delay of choice if I remember correctly. He switched to the Korg's later, probably because of dependability and also because you can more accurately dial in delay times.
The sound of the Memory Man's is great, second to none, mostly due to the fact it's a bucket-brigade analog delay, therefore limited in delay times but has a lovely way of degrading the sound with each delay instance. Digital delays have to imulate this degredation.
This was one of Jimmy Page's favorite delays as well, along with the Maestro Echoplex.
The Line 6 family does a nice rendition of the Memory Man, called Analog Delay w. Mod if I remember correctly, should give you some idea of how it sounds.
But a note on tap-tempo delays, In My Humble Opinion of course:
While it is true that you can tap the tempo to your performance live, it gets you Close, but the Cigar only comes when playing with a click-track or a backing track.
Note that this does mainly apply to songs that are really delay-dependent.
Playing a song like Where the streets.. etc, with the delay "almost right", (within a few milliseconds) simply doesn't work.
It has to hit exactly on the notes, otherwise it simply messes up the song instead of adding to the percussive/groove/drum-side of the song.
A workaround the click track would be to place your guitar amp close to your drummer so that he could follow the tap'd tempo from your playing.
Which is the way I believe U2 did it extremely early on. As Edge once put it: "...at one time i became the time-keeper of the band because of the delays for my guitar..." or something like that.....
hope this helps,
cheers,
LP