if you want full-blown geodatabase capability (Coded Value Domains, Relationship Classes, Topologies, Geometric Networks, etc blah blah, without the complexity or admin overhead of relational geodatabase, AND/OR you want the fastest drawing, cursor, and geoprocessing performance, File Geodatabase is the way to go. Local disc access is much faster than a remote relational geodatabase. FGDB, like shapefiles, use floating point coordinates, not integer, for better and worse. FGDBs can be fragile, being complex, binary, and proprietary, so keep lots of backups. Shapefiles are the dumbest but the most widely supported, and can be quite speedy to work with too. Relational geodatabases allow you to use SQL, including spatial SQL, which can be quite flexible and convenient for ad-hoc analysis or applications.

if you want full-blown geodatabase capability (Coded Value Domains, Relationship Classes, Topologies, Geometric Networks, etc blah blah, without the complexity or admin overhead of relational geodatabase, AND/OR you want the fastest drawing, cursor, and geoprocessing performance, File Geodatabase is the way to go. Local disc access is much faster than a remote relational geodatabase. FGDB, like shapefiles, use floating point coordinates, not integer, for better and worse. FGDBs can be fragile, being complex, binary, and proprietary, so keep lots of backups. Shapefiles are the dumbest but the most widely supported, and can be quite speedy to work with too. Relational geodatabases allow you to use SQL, including spatial SQL, which can be quite flexible and convenient for ad-hoc analysis or applications. Personal GDB hasn't been worth monkeying with since the advent of FGDB - buggy, slow, file size limitations.