It’s dependent on where you live for sure. Benefits of tap water include extra Calcium and Fluoride (purposely placed to some extent for drinkers benefits). Problems include impurities mainly from your piping. This is especially bad if you live in old regions that used lead pipes. Most bacteria are killed off by the Fluoride and Chlorine in the water (as a result taste isn’t always that spectacular). However, depending on which industrial processes are nearby, chemicals such as TCE (trichloroethylene…a damaging nerve toxin) and other chemicals may leech into water systems.
But, Bottled water must only meet minimum standards. In fact there have been companies that take water directly out of a clean river and bottle it (thus spending no money on purification) and still charge $2 per bottle. It met the standards so it’s safe, but I don’t like to be ripped off.
Personal preferance…Filtered water. Either Brita or other filters attached to the sink.
BTW, hot water dissolves more impurities esp. heavy metals. As a result, cold water is generally much cleaner. I’d say your doing a good thing by boiling cold water. This practice should be used even for cooking your food.