The primary feature that differentiates delays is what effects you can apply to the delayed signal.
The delayed echo is typically not an exact replica of the incoming signal. You'll have the ability to add one or more effects to it, and that's what distinguishes one delay plugin from another on a technical level. Those effects may include the following:
Filter: nearly all delays give you a low-pass filter. The next step up from garden-variety delays is multiple filter types.
Pitch modulation: delays that attempt to emulate classic tape delays can modulate the pitch of the delayed signal. Some give you a lot of control, some just have a button labeled "TAPE".
Distortion: some delays let you dirty up the delayed signal, again mainly to emulate vintage tape machines. Some give you lots of controls, some just have a knob labeled "distortion".
Tempo sync: many delay plugins let you synchronize the delay to the project tempo, such as quarter- and eighth-notes. The next step up in sophistication is more unusual synchronization factors such as a dotted eighth or a one-third note, and non-sequential patterns.
Panning: many plugins let you send the left delay to the right channel and vice versa for your basic "ping-pong" effect. The next step up is the inclusion of options for setting the pan position of each echo independently.
Chorus: adding chorus to the delayed signal gives an effect similar to tape flutter, and can help intensify one of the effects we use delays for, which is creating width on a track.
There are delays that offer all of the above and then some. Which leads to the next differentiator: the user interface. All those options can make for a confusing experience, to the point where you can end up relying on pure serendipity to stumble onto a pleasant setting.
RP-Delay, for example, is one plugin that has oodles of features but seems particularly difficult to dial in when you have a specific echo effect in mind. Timeless has so many options you have to make a serious investment in learning it before it starts earning its keep. My point is that having gobs of features isn't the only factor, because they don't do you any good if you can't figure out how to use them.
The easiest-to-use delay I know of is the venerable Sonitus Delay. With it, I can dial in an imagined effect in seconds. It does lack some features that have become widespread since the Sonitus came into existence back in 2003, and it has a couple troublesome bugs. But I still like it a great deal.
Another one that manages to keep sophisticated features simple is
Ricochet from Audio Damage. It's cheap ($49).