I've heard about uses of a short delay instead of reverb. When might this be better than the original effect? And what delay settings provide a reverb-like sound?
Reverb and delay aren't completely unrelated effects - reverb can be thought of as a network of many short delays.
While reverb can provide a realistic simulation of an acoustic space, using a lot of it will smear the effected signal in the time dimension, and tend to push it back in the mix, making it sound more distant. If reverb is applied to a signal with a lot of lows and highs, this can have the effect of smearing the whole mix; if you roll off the frequency extremes of the signal that is routed to reverb, the effect of pushing the part back in the mix is even greater. High levels of reverb can also cause problems with intelligibility when applied to a fast vocal.
A simpler traditional delay does not produce such a realistic simulation of acoustic space, but the effect of the discrete echoes can still produce the illusion of space without creating such a 'mess'. Think of dropping a glass on your kitchen floor - less messy if it breaks into a few big pieces rather than shattering everywhere!
So, one time to try delay instead of true reverb might be if you want to keep the effected part forward in the mix without losing definition or intelligibility. Another time might be when you are playing live in an environment that is already reverberant, such as a large hall, where adding even more reverb would cause problems.
To simulate reverb with delay, try times between 100 and 500 ms. Below 100ms, you start to get the same smearing problems that you do with true reverb, without the realism that a true reverb provides; above 500, and the repeats will start to get 'divorced' from the dry signal, losing some of the illusion of it 'happening in a space'.
Try moderate levels of feedback, and also try rolling off the low and high end of the repeats if your delay allows. Analogue- and tape-style delays often have naturally limited bandwidths and can be excellent for producing pseudo-reverb effects.
Of course you don't have to choose one or the other - you can use both! Routing a delay into a reverb is a great recipe for producing a subjectively 'big' sound without having to use too much reverb.
Both give the effect of ambiance to your sound, but in a mix this may be overwhelming.
When might this be better than the original effect?
Reverb will obviously "smear" the sound and give it dimension, versus delay's ability to replicate with clarity (especially with the effect of ducking). Both are quite similar with focusing on guitar with a solo track, however when more sound is added (in a band setting, for example) the "smear" of reverb may be too distracting.
This is often why you hear people recommend delay over reverb, especially in a band setting. You still get the dimension added to the sound, but clarity still remains between notes.
And what delay settings provide a reverb-like sound?
To achieve a reverb-like delay setting keep your ms time low (100-300) and your feedback settings up so you hear a controllable tail to the end of the note.
This is all relative to the effect's intention. If we're going for a rootsy blues effect, reverb is best as that's the original intention of "that sound". However, especially in this case, if we're talking about adding an effect of spaciousness, delay and reverb can be substituted for each other depending on the denseness of the sound.
Delay and reverb sound quite different. There is no "better" - they just do different things.
The best way to think of the difference is to imagine a delay as an echo coming back from a wall, and a reverb as multiple echose coming back from objects at all sorts of distances - instead of one simple echo, you get a run of sounds from the initial echo through to a long tail of echoes, sussurations and noise.
A basic delay will not sound like a reverb even when set to a very short delay with multiple repeats.
A good delay may allow mixing of reverb effect, but normally they are two separate effects that you can add in your effects loop.
I use delay and chorus on my board as my standard sound chorus only just on, delay set as others have mentioned above, I have another delay and chorus that I use as full effects. I ditched reverb 10 years ago when I was gigging on the advice of the sound tech on a sound check that night I played the first half of the set with the second without, the tech recorded out set, a week later when I picked up the CD the difference was really noticeable and the guitar cut in to the mix better.