Can I move my 14 Gal or Half Barrel Chronical by the handles when full?

No.

While you can on the 7 Gal Chronical, it is not recommended for the 14 Gal or Half Barrel Chronical.

The handles are spot welded not riveted.  

We do have 3/8" threaded holes at the bottom of the legs to put casters on so you can wheel it around.

If you need to pick it up and carry it, you can have two people lifting both the legs and handles, focusing more force on the legs.