register_sidebar_widget is deprecated since version 2.8

Well…

register_sidebar_widget( $name, $output_callback, $classname );

vs.

wp_register_sidebar_widget( $id, $name, $output_callback, $options, $params, ... );

It is simple enough to check the Codex entries for each:

Beyond that, I am not quite sure what the question is. You might want to look into the register_widget function instead of either of those, though.