Christophe,
Glad to hear Facebook is working well for you. As for Twitter, I'm not sure why the data isn't coming in properly. Is automatic registration enabled in JFBConnect? If so, then the account should be created normally and the registration page should be skipped.
A couple of good tests to help narrow things down are:
* Set the Registration Component to "Joomla" in JFBConnect and test if that automatically creates the account.
* Go through the registration procedure and then logout. Login again with Twitter to see if you're logged into the proper account. If not, it means the right data isn't coming back from Twitter. If it does work, it means that data is coming back, but not all the profile information.
Either way, double check our configuration guide and make sure all the settings in your Twitter application are correct.
I hope that helps you get started.
Thanks,
Alex