Please note that the FamilySearch and Antenati database overlap for the most part but are not identical.
For instance, Antenati deals only with civil records - birth, marriage, death, but also yearly and decennial indexes (very useful when the primary source is not available, even if they are secondary ones) and marriage processetti, which are the paperwork prior to the marriage itself, usually a wealth of info that does not appear in the marriage act itself. They are all freely available, but not all of them indexed (that is being done through partnership with FS, but only for B/M/D so far).
On the other hand, if you search a particular location through the "Catalogue" option in FamilySearch, you may get lucky and find catholic church records that are not available anywhere else. Also census records (not indexed usually) that are not on Antenati and may be extremely useful . Many of them are freely available at home, some others at a Family Center or affiliated library. Some of the church records go back to the 1700' and even the 1600'.
Good hunt!