A water wheel can not have more than 75% of the blades in contact with water at any point (or it would slow it down) and it is rarely practical to have more than 30% of the blades in contact with water.

A turbine in a vortex has 100% water-blade contact all the time, which means it can transfer more power with a smaller size and cheaper materials.

A well designed waterwheel could be pretty efficient in these cases, too. Waterwheels tend to lose out when hydraulic head (water drop distance) is too big to construct a practical wheel.

As other people have said, the advantage here seems to be that you get a high rotation speed out of a low hydraulic head. A waterwheel in this case would have lower RPMs, and so require more gearing etc. to be efficient for power production.

In general, turbines are preferred because the moving parts are smaller - rather than having a massive spinning wheel, you just let gravity provide the water pressure, and have a much smaller turbine blade do the spinning.