Browser-based OAuth flow (like Facebook's new iOS SDK -- the one that avoids using embedded webview) has two advantages:
1.) Single sign on. If you're already logged in to the site in the browser, you don't have to enter your user/password again. Also, if you don't trust the app invoking the web browser, you can always exit the app and pre-login to site with the web browser before running the app again.
2.) Optional interstitial pages. Sometimes, your account may be accessed from some questionable location. The OAuth flow enables challenging users with additional security questions before giving authorization to the app (e.g. Facebook's identify-your-friends'-faces challenge, enter-your-birthday challenge, etc.)
1.) Single sign on. If you're already logged in to the site in the browser, you don't have to enter your user/password again. Also, if you don't trust the app invoking the web browser, you can always exit the app and pre-login to site with the web browser before running the app again.
2.) Optional interstitial pages. Sometimes, your account may be accessed from some questionable location. The OAuth flow enables challenging users with additional security questions before giving authorization to the app (e.g. Facebook's identify-your-friends'-faces challenge, enter-your-birthday challenge, etc.)