It seems as though lately every app that I test includes some form of social network integration. According to a Gigom article, which cites data from Localytics, more apps support sharing with Facebook than other social networks, but Twitter users more actively share by a factor of 3 to 1.
According to data gathered from January to July, 2011, 20 percent of all mobile apps have the ability to share with social networks. Ten percent of those apps only share with Facebook, and only one percent of apps just share with Twitter. Nine percent share with both Facebook and Twitter.
While overall Facebook users generate twice as many sharing events as Twitter users, on average each Twitter user shares three times more events than Facebook users. I am personally not sure about the significance of the per user averages.
What I conclude from this information is that social network integration is now expected in mobile apps. If a developer has to pick only one social network to support, they probably want to pick Facebook over Twitter unless they are seeking to increase sharing per user. Ideally, mobile apps should integrate with both Facebook and Twitter.