A good answer would be quite long. The short answer is yes. Each of Helm and Icicles offers features not offered by the other.
They are not necessarily alternatives/competitors. You can use both.
Wrt your question about matching candidates, there is no difference wrt showing all candidates. IOW, Icicles too will show all candidates anytime you like (including initially, without hitting any keys). "candidates that match your current input" is completely general, and includes the case of your input being empty, which means all candidates are included.
Here is a high-level list of the most important Icicles features. Some of these have also been added progressively to Helm over the years, if in a different form. Other answers to your question might help more wrt what Helm offers.
FWIW, I seriously doubt that a discussion of what you can or cannot do with each of these packages is useful here. My suggestion, if you are interested in exploring Icicles, would be to try it.
But just as using Helm benefits from (or implies or requires) a different mental model (mindset) from using vanilla Emacs, so does using Icicles. To try Icicles or Helm, it is helpful to try to do things the Icicles way or the Helm way, respectively.
Icicles is not Helm, and Helm is not Icicles. Neither tries to be the other. Expecting to use one the same way you use the other would (a) likely be disappointing and (b) make you miss a lot (including the point of the design). It's a bit like an "avid"
vi user taking a look at Emacs (or an Emacs user taking a look at
vi). If you really want to check it out then try to get into its approach/POV, instead of asking how to reproduce a particular behavior or effect you are used to and are "avid" about.
Deciding to take a look at Icicles based only on a feature-list comparison with Helm would take the fun out of learning Icicles, IMHO.
It's kind of like learning a new math subject: you just have to go with the flow of Let x..., to give it the benefit of the doubt. See what happens next and subsequently discover why it might be interesting and what you can do with it. If your attitude from the outset is "What good is linear algebra (or group theory or...)?" then I'd say don't bother - it might not be any good to you at all.