Drink what you like but ground water is far worse in regards to contamination. It has not even been filtered by anything with life.
It is the worse choice because not only do you have contaminants in their raw state, you also have large amounts of unusable minerals -- the prolonged effect is arthritis, kidney failure, and hardening of the arteries. My grandparents drank hard water and took calcium supplements their whole life. One died of Rheumatoid Arthritis and the other is still living but is as fragile as a glass statue. If you're still young, you better find the truth soon.
Drinking ground water for mineral nutrition purposes is an absurdity of reason. Do you realize how much hard water you'd have to drink daily to even come close to an adequate supply of calcium? Probably over 7 gallons per day (enough to kill you twice). Anyone who is suggesting they are drinking water for nutritional purposes does not understand the very basics of water composition, human nutrition, or the point of water.
The claim that distilled leaches good minerals is propaganda or misinformation. Quite the contrary in my experience. Distilled water (because of its purity and "slippery" nature) feeds the cell with organic nutrients better than any other water. Ironic huh? Good luck.