You should be able to use the new facebook SDK to implement facebook single sign-on. Thus, if the user already has the facebook application installed on their device, they are already logged in, and this is a much better experience than the old popup popup implementation. For your application, you must provide access to your account, but besides that the ugly sign screen is not used.
If they do not have the facebook application installed, it will launch in the browser.
Both methods use URL processing to return to your application after authentication.
Read more about this here: http://developers.facebook.com/docs/mobile/ios/build/#implementsso
In terms of implementing your own login screen instead, it is against Facebook TOS, because they want a consistent and familiar sign in the platform to avoid common problems with phishing, etc. To a large extent, they insist on educating their users only to provide their usernames and passwords to legitimate pages.
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