It all depends on the sound you are after really. You really have to listen for the repeats to hear the difference. I've owned and played everything from the Boss DD-3, Boss DD-6, EH Memory Man, Line 6 DL4, MXR Carbon Copy, etc... The digital delays to some sound "sterile" because they are VERY CLEAN and simply repeat the note(s) played with little to no coloration. Tape delays have the most coloration to my ears with a lot of warmth, warble, and even distortion to the repeats. An analog delay sits nicely between the two with a little warmness to the repeats but also relatively clean. The DD-3 is more "analog" sounding than a lot of digital delays, the Line 6 DL4 gives you good representations of tape/analog/digital echos, and the MXR or Ibanez AD-9s give you that classic warm tone. Keep in mind that most digital delays are more flexable and have longer delay times. That was a minor gripe about my old Memory Man. It sounded incredible but I wish it had longer delays and didn't distort as easily. Good luck!
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.