I could not find statistical information so I have had to rely on more qualitative sources:
Lifehacker:
http://lifehacker.com/5886059/the-best-news-reader-application-for-linux
Android Quality Index:
http://android.qualityindex.com/charts/19000/top-5-news-aggregator-apps-on-android
The Financial Times recommends these apps:
Google Currents
Livestand
Editions
Zite
Pulse
(Jan 20, 2012 PERSONAL TECHNOLOGY - CHRIS NUTTALL)
These were released in the last year so are fairly relevant.
If I had the time I would monitor usage statistics myself to elicit more empirical information.