Cross-App Relationship v. Sync Table

There are a few downsides to doing cross-app relationships.

One: Any user of the child apps, also has to be a user of the parent app with permissions to see the information of the said "facility".  Otherwise the dropdown fields appear blank.
Two:  I've heard that this can cause performance issues, especially if you want to pull summary information back to the facility

The big question is:  Why do you want them to be separate apps, why not keep it all together?  This will give you a lot more flexibility down the road and avoid any synced tables (which is very finicky, and not very easily modified) 

Personally I never recommend the sync option because you cannot add any data to that table.  I always, unless for a better reason, would recommend table-to-table relationships using Cross Application Relationships.  Also you can send data back to the parent that way without issue.

When you build the cross-application relationship, you will set the access permission to the highest-level role to ensure that the connection and lookup fields work correctly.

I have many QuickBase customers using centralized-applications for storing centralized-data common across a business; and it is generally the smarter way to structure data to avoid a) duplication and b) bad data entry.

Syncing severely limits what you can do with the data in the synced table, and generally requires a higher level of knowledge for connecting data to the synced table.  If you want to "replicate" a data table in an application so that you can set other characteristics and attributes to it; consider instead Table-to-Table relationship imports which can copy the data from your "master" source, but still provide you the flexibility of a customizable table.