Sprite isn't shipped very much in bottles. The soda companies are very good at shipping concentrate and then adding water locally. Bottled water is different in that the entire transport occurs as water.
I don’t believe your last sentence is correct in the case of brands like Dasani that are just filtered tap water. And for drinks other than water the bottles still have to get made and disposed of. Again, they are all just bottled water with a little bit of extra stuff in them, so whatever impact bottled water has, they all must have as well.