Apart from the vertical presentation (which icomplete will apparently soon
have), does ivy have a feature that icomplete does not have? I can't find
one myself, but perhaps I'm missing something.
Does icomplete support different actions on the completion?
For example, if I want to insert a file name with completion, I can do C-x C-f (counsel-find-file), use ivy-completion to get the name, then M-o pops a list of actions and tells me to press i to insert the file I selected. For such an action which I do quite rarely, I find it easier than remember how to invoke insert-file-name (including the name of the actual function).
Counsel offers many more actions (which I don't use), including open-literally and open with an external program, and also filesystem actions such as copy, delete or rename.
Other actions are offered for buffers, for isearch matches, etc.
To me it feels very non-intrusive, what you don't use won't come to bite you. But it also goes beyond the scope of a mere completion mechanism.