The handle in the water bottle can make cleaning it a bit difficult if some sediment gets in there. No handle in a Better Bottle.
There are thousands of formulations of PET (#1) plastic. I believe that the BB plastic is designed for alcohol, whereas the water bottle is not. Also I believe that some water bottles have been #7 (Other) plastic (not sure if these are still being made). Would definitely avoid the #7 bottles for winemaking.
Finally, water jugs are not designed to accept a bung. The inside of the neck is not necessarily smooth or correctly shaped, so a proper bung seal may not occur. Whereas the Better Bottle neck is designed to accept a bung. The water jugs pictured look like they have screw caps (although very hard to be certain in the picture). If they are screw caps should be able to drill an air lock hole.
Personally I would not use water jugs.
Steve