Is the rooted hack for Move to SD card better than the option built into the Android Phone OS?
The "Move to SD card" neither moves the app (APK file) nor the complete app data.
It just moves the additional media files and data (that doesn't pose any security risks upon revealing to user) like Images or Graphics or whatever.
(And all apps do not provide this option. It depends on the app developer.)

These moved data can be found in the Memory Card in a directory named Android/data .

And yes, the rooted solution moves the complete app and app data into your memory card, which completely lessens the burden.
But you have to create a separate EXT2/EXT3/EXT4 partition first in your memory card (using softwares like MiniTool Partition Wizard) and then use an app like Link2SD (as @Tamoghna said) or Mounts2SD.