(2005) compared their results with Model 4 using "intersection" by looking at AER (with the "Sure" versus "Possible" link distinction), and restricted themselves to considering 1-to-1 alignments.
"union" and "refined" alignments, which are many-to-many, are what are used to build competitive phrasal SMT systems, because "intersection" performs poorly, despite having been shown to have the best AER scores for the French/English corpus we are using (Och and Ney, 2003).