Is the rooted hack for Move to SD card better than the option built into the Android Phone OS? What I have found recently: In order to save space on my device (Galaxy S5) I attempted to use the 'move to SD card' option. This has not really helped all that much. It seems that it uncompresses an application, making it a lot larger before moving a chunk of it to the SD card.

What I am asking is about the option that is available via a rooted phone. Does the rooted version offer a better solution, such as moving more of the app to the card? Or is it not worth the effort to root the phone for that choice?

My phone is I am certain long out of warranty so not really worried about that.

It is clear to me there also may be multiple different tools that do this. It would be helpful to find which may be the best choices. Thank you in advance.
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.