What extension is by now the most succesful in displaying CiviCRM content in a mobile app?
(If you have any personal experiences, please tell about them...)
The CiviMobile extension is poorly documented, but after a while I figured out that it uses profiles to choose which fields to display. Also different profiles for each contact type: Individual, Household and Organizations. It took me more time before I figured out that it used the restricted profile_ids 4, 5 and 6, which can be edited to add more fields.
Then I could also use some of the fields from Summary fields, to display relevant contribution informations as search result on the contact.
I don't think that apps are as common as using responsive design for the site and then creating special pages that don't put too much onto page.
We have found the Extension CiviMobile quite good. Have you checked it ?