Do you use Google Optimizer? If not, go there. Setup a test to compare sign-ups to your app between OAuth and Basic Auth. Give 50% the option to sign up with OAuth; 50% the option to sign up with Basic Auth. The results may surprise you.
In my tests, I have found statistically significant more signups from Basic Auth than from OAuth. But maybe that's not so surprising. Users are accustomed to giving username/password information, even to "foreign" apps. They are far LESS accustomed to going to Twitter and hitting some bizarre "approve" button. To them, that's far more invasive and often more cumbersome (they may have to relogin to Twitter) than simply having to retype their Twitter username/password. The net result from using OAuth for third-party developers is fewer sign-ups than from using Basic Auth. Plus, as recent unannounced changes by Twitter have indicated, Basic Auth is far more reliable. (I am talking about the several day outage of OAuth a few weeks ago; and today's unannounced API change to OAuth which breaks multiple Twitter interface libraries.) SO... user response, Twitter unresponsiveness (when it comes to unannounced API changes), and other factors are prompting me into the weird position of deprecating OAuth and promoting Basic Authentication. Weird, eh!?