I work with ArcGIS 10.1 SP 1 (on Windows 7), and I tried to export a feature layer to a personnal geodatabase using "right click in the table of content > data > export data". However, when I select "file and personnal geodatabase", only the file geodatabase are visible (though the mdb are visible in ArcCatalog). Of course, the obvious workaround is to use "feature class to feature class", but I would like to know why this "data > export data" is disabled. Is this because .mdb will disappear from ArcGIS in a near future ?
I am unable to test this at 10.1 but I just tried Export Data on a layer (with shapefile source) in the Table of Contents at 10.2 on Windows 7 SP1 (64bit) and both personal and file geodatabases show up in the browse dialog when I set Save as type to "File and Personal Geodatabase feature classes".
I will be surprised if this was not working and went unnoticed at 10.1 so I would recommend that you describe your environment more fully i.e. ArcGIS service packs, Windows OS (including service packs) to see if someone can test on an "identical" configuration to yours.