While every water source is different, there are certain common water problems associated with each type of water source.
Surface water needs to be aggressively treated. It's susceptible to contamination by pathogens and toxic substances, both natural and man-made. Surface water will often have lots of bacteria, sediment, and low pH.
Well water is somewhat more protected than surface water, since it's been filtered through the soil on its way to the aquifer rather than captured from the surface. However, since it's had more time in contact with the soil, well water tends to have higher levels of mineral impurities than surface water. Any new well drilled should have had a potability test completed by a state certified laboratory before it was put into service. But well water quality can be poor even if it's technically potable, and water quality can change over time. High hardness and sediment are common in well sources, and other issues like low pH and foul odors can be a problem.
Municipal supplies are typically tested and treated by third parties, but they're not without their problems. The water chemistry in a municipal supply is tailored to protect the water mains from corrosion, and to minimize bacteria growth. That usually means hard water with lots of chlorine, and sometimes a chemical corrosion inhibitor. Sediment is typically removed at the treatment plant, but the water main itself may add sediment or metals to your water downstream of the treatment plant.