When you say "Catholics believe something different" of whom are you speaking?  You cite a Vatican website.  Are Catholics only those who are members of the hierarchy and clergy?  Only the 4% world-wide in this category of Catholics?  What about the other 96%?  What do they believe?

The Problem with JP II's commentary is that he, like too many of the clergy and hierarchy place an over-weighted on the differences between men and women.  Actually, the difference is purely biological/sexual.  In Catholic theology if something is different, then it must be treated differently.  Women's sexuality is different than men's so women are different and they must be treated differently.  
This view of theology fails to see how many other areas in which women and men are similar.  It fails to count dedication, perseverance, desire to serve, willingness to sacrifice all for the sake of the kingdom.  Mostly, it fails to value the great love of God and neighbor that can be common in both genders.