The advantages of a constant dribble of water into the tank, with an over flow are:
No worry about incoming water temperature - it isn't enough water in an hour to change the tank temperature. No problem with chlorine/chloramine - I used a all house water filter with a carbon filter in it to remove most of the chlorine. Tank water level is always the same. Fish are never subjected to big changes in water parameters. No schedule to follow for water changes. If the overflow plugs you see a very slow increase in water level, so no problem with overflowing the tank.
Disadvantages include: While you can get 50% of the old water removed per week, there is never a time when that happens in one day. You never lower the water level if that would help in keeping tank clean. It uses more water per 50% change than any other method. You either do something about the constant dripping noise, or you collect the drained water outdoors, and have to empty that container daily. The fish never get the "high" that a sudden 50% of new water gives them.