The answer is probably simpler than you expect. :)
Google-api-java-client is a new library from Google. It can access more APIs and run on Android. However, it is still in beta. On the other hand, the gdata-java client is stable and more mature, but does not work on Android.
If you use gdata APIs and you do not need to run on Android, I recommend that you use the gdata-java-client library. If you need to run on Android, google-api-java-client
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