(EDIT - I changed this from a question asking for an App for the 'general contact/member to a more generic one that hopefully gives good enough across the whole range of scenarios)
There are several questions about Apps that i have found eg - CiviCRM on mobile phone - What is the best approach for using CiviCRM as an app on mobile? - CiviCRM on mobile phone
My sense at this early point of discovery is that most effort has been going in to Apps for the admin/organiser, rather than just for a general user/member who may want to - view and update their profile and membership. - see their relationships and click through to those relationships eg employer, region and club. - search for and register for events through the app
Hence this question will hopefully flesh out what features each offers and what particular scenarios they may be best applied to.