Briefly, the standalone version has more features. However, each version has its benefits.

Standalone version

Has more icons. Apple made us exclude all logotypes, so there are no Apple, Windows, Android or Facebook logos.
Supports paid icons from the Icons8 website. Apple prohibits any reference to commerce other than within the App Store.
Is updated more frequently. Releases are immediately uploaded to the website, whereas the App Store review can sometimes take weeks (We have to resubmit the App and so on).

App Store version

Easier updates. Standalone version notifies you about the new version and downloads it, however it doesn't do it automatically like the App Store does.
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