Bottled water is usually better for your health as it doesn't contain all those chemicals like your tap water usually contains if you're on city water.
City water from your tap is usually unfiltered water with chlorine and fluoride in it while most bottled water does not contain those chemicals which can be harmful to your health.
I always drink bottled water because my city tap water has chlorine in it that I can easily taste and it hurts my stomach but the bottle water doesn't hurt my stomach nor can I taste any chlorine in it.
Bottled water is essentially tap water from a factory but it's filtered using commercial type water filters so it's cleaned better and tastes better.