The best thing about tap water is that it is still regulated by law. Whatever county or city that is supplying that water must constantly test it to stay within those regulations. But tap water is also imperfect because a lot of things get into tap water that treatment facilities cannot remove. They can kill pathogens but they cannot take the synthetics out of the water.
On the other hand, the trouble with bottled water is that its un-regulated. This basically means that nobody knows what kind of water they are putting in those bottles. Many water companies have even been guilty of taking regular tap water and selling it to us consumers. The most shocking thing about bottled water is the "bottle itself." If you test the water in a plastic water bottle, you will find traces of plastic in the water. Sadly most companies are allowed to essentially introduce chemicals in products without having to pass health regulations.
As an example let's use a mother heating up a milk bottle for her child. When she wakes up in the morning, and her baby is starving, and she takes the bottled breast milk and puts it on the stove top and warms it up, the plastic in the bottle can actually be melting into the "breast milk itself" and many times this happens faster than it would at room temperature.