Single sign on between different Drupal versions
With the drupal-6 site override hook_login_validate() and write your own authentication mechanism. Simpler than it sounds, as any function that returns TRUE or FALSE based on success will work. It could directly access the database or connect via a JSON web service to the drupal-7 server. I described how to implement authentication via JSON on stackoverflow.

function mymodule_login_validate($form, &amp;$form_state) {
   $username = $form_state['values']['name'];

   // do if condition to see if your authentication is required.  
   // e.g. you might want to keep the drupal administration users.
   if (_mymodule_use_webservice_login($username)) {
     // We are logging in using service.
     if (_mymodule_validate_password($username, $form_state['values']['pass']) {
       user_external_login_register($username, 'mymodule');
       user_authenticate_finalize($form_state['values'];
    } // else drop through to the end and return nothing - Drupal will handle the rejection for us
   }
} else {
    // Username is not an member number, so use standard Drupal authentication function
    user_login_authenticate_validate($form, &amp;$form_state);
}


_mymodule_validate_password() is where the authentication occurs and the only other function you need to implement. See the stackoverflow site for calling a JSON web service. Try to use SSL as passing passwords over SSL is not great, although your main site may not be SSL anyway. 

Implementing the web service is a function return TRUE or FALSE - drupal_json_output. You need to set up a menu, with a function callback. The function callback would call user_authenticate().

You could also try one of the SSO modules. http://groups.drupal.org/node/182004. It is usually good policy to not implement your own security code so that the code gets tried as much as possible.