There is an answer (from Grist)
Quote: “When it comes to water use, the difference between manual and machine practices was even starker: Hand-washers used 34,200 gallons of water to a dishwasher’s 16,300 gallons over 10 years. In short, a dishwasher that’s being used correctly emits 63 percent fewer emissions in its entire lifecycle — including manufacturing and disposal — than a typical sink.
However, there’s a silver lining for resource-savvy hand-washers. If you happen to have a two-basin sink, filling one basin with hot water and the other with cool water, and then soaking and scrubbing your dishes in the first and rinsing them in the second — and then letting them air-dry — was the least energy-intensive method out of all the techniques the researchers tested. The two-basin method only produces 1,610 kilograms of emissions over 10 years. Adopting this technique leads to a 249 percent reduction in emissions for people who wash dishes manually.”
Only if somebody would complete and publish these types of comparisons for all consumer goods / products …