The mobile version is pretty good and with ios 5 you can have it on your homescreen. But I really agree that tere should be an app that gives us some extra features than the mobile version:
Firt of all, it should not be necessary to log in every time , some sort o stay logged in button should exist.
Then thy should make it possible to reply to messages, so far it only let's you send a bee message to that person when you hit reply...
Thirdly in the alliance forum, there should be some way to see that people have commented on a topic as I need to go through everywhere ad to find new stuff...
Other than this it is great
For everyone who needs some I the inflame features that mobile version does not allow, you should download photon, an application that can use flash and they also have the awesome feature of changing from touch ( normal function like safari) to a mouse ( drag it around at will and you can click by double tapping anywhere and finally drag mode whih allows you to move around in map mode!
This app does cost money but is really worth it
But I still believe there should be a grepolis app with the features mentioned above ( but being a free game, it should be free)