3 solid reasons to use digital delay instead of analog
Switch to digital and you'll enjoy using the delay effect for guitar a whole lot more.
Delay is one of this electric guitar effects that I consider must-have for any player regardless of skill level. Whether you've been playing 3 months or 30+ years, you need it. Yes, I said need. In fact, if I were forced to use just two effects and nothing else, it would be compression and delay, in that order.
Regular analog delay is cheap unless you go for something like the Boss DM-2w Waza Craft, considered by some to be the "ultimate" analog delay pedal...
...but I don't bother with those because there are 3 things about upper tier digital delay pedals that really make them worth owning.
These are the 3 upper-end digital delays worth checking out, and then I'll tell you 3 good reasons to own one no matter which you get: NUX Duotime (good), Boss DD-200 (better), Boss DD-500 (best). Most would get along with Duotime or DD-200 best. The DD-500 is absolutely nuts in what it can do, but is also complex; the two others are easier to get along with.
Reason #1: Works better with more live rigs and home recording
Digital delay does not make noise and is whisper quiet when on. Analog delay, regardless of how much you spend on one, will have noise you can hear, and that's just the nature of how analog works.
Reason #2: The emulation of the old analog delays is far better than you realize
The upper-end delay effects mentioned a moment ago all have the ability to emulate old analog sounds very, very well. The tape-style echo is there that a lot of players want, but that only scratches the surface of what you can get.
Reason #3: You can set a precise repeat rate
This doesn't sound like a very fancy feature, and it's not, but once you have it, you'll never want to go without it again.
Setting the repeat rate on an analog delay pedal either ends up in being too fast or too slow. Or, if you somehow magically get it just right, don't you dare turn that knob or you'll never get it again (this is especially true with the DM-2w, which has really sensitive controls).
On the digital, you have not one but two ways to set a repeat rate. Manually, by entering in the millisecond rate, or by tapping the tempo. You will notice that each of the 3 pedals I mentioned have TAP as the right side footswitch.
In a live band situation, you can tap the repeat rate for whatever your drummer is playing. Very convenient.
With home recording, you can match the delay repeat to your recording software metronome by millisecond or by tapping the tempo out. Easy.
It costs more but it's worth it
The upper tier delay effects are not cheap, but at the same time not terribly expensive. The only one where you feel the sting of the price is with the DD-500, but you do get what you pay for as it is a seriously advanced delay effect. Again, the NUX or the DD-200 would suit most players.
It's the 3 reasons above that justify the cost. The better digital models do work with more amps and home recording environments, all the old-school emulation is there (and works well), and most importantly you can set a precise repeat rate.
Again, that precise repeat rate setting doesn't seem like much, but believe me, it matters; that's the reason you get the upper tier delay effect to begin with.