ArcGIS for iOS is no longer under development (feel free to correct me, but I've not seen an update for quite a while).
ArcGIS for iOS allows us to send links to our users, to take them directly to their map. A very helpful feature. Collector allowed this for a time. At some point this ability was removed.
ArcGIS for iOS will find and open any AGOL (ArcGIS Online) / Portal map, regardless of content. Collector will only open maps that contain at least one feature service. In other words, maps without a feature service are not found by Collector.
Collector has a setting for desired GPS accuracy while ArcGIS for iOS does not.
Searching for maps can be focused to just your AGOL organization or your Portal in Collector. I haven't found a way to focus the searching in ArcGIS for iOS. In ArcGIS for iOS, searches for maps return quite a few unwanted results.
Merry Christmas,
Paul Lohr