Yes the front load washing machines use less water to clean the same amount of laundry than a top loading washing machine does.
I'm not sure why exactly the front loading washing machine use less water than top loading washing machines but after buying a front load washing machine and using it my water bill was less and showed I used less water using the washing machine the same amount.
The front load washing machines are also more energy efficient as well and use less electricity to clean the clothes and laundry and I find that my front load washing machine gets the clothes and laundry much cleaner.
Front loading washing machines use 13 gallons of water and sometimes less where a top loading washing machine will use around 20 to 30 gallons of water depending on the load size of laundry in the washing machine and how big the washing machine tub is.
Another benefit of a front loading washing machine is they spin faster which helps to extract more water from the laundry which cuts the drying time down.