Undulating waves are created with air pressure or water paddles. High pressure air, or a moving paddle displaces water at the deep end forming a wave. In simple terms, the air model is a giant fan that creates a depression in the water, and the water displaced from that depression has to go elsewhere - creating a ripple. So in simple terms the mechanics, and cost to operate is fairly simple.
In terms of construction, these displacement style pools really only require the pool itself, and connected filtration, with the fans or paddles placed at one end.
A water dump pool uses a lot more energy to operate. I'll use Thunder Bay as an example - since it was what I could find some stats for online - it uses a 100, 200 & 300 horsepower pump to move water through 3 metres vertical, along a length of 9 metres of pipe, into the dump reservoirs.
On the numbers - it dumps 341,000 litres into the 7.6 million litre pool to cause the waves. To generate waves of a reasonable frequency, these pumps have to move that water constantly - achieving approximately 150,000 litres per minute at normal speed.
You're then running a hydraulic system to open and close the reservoirs (there are eight chambers at Thunder Bay, so 8 separate hydraulic doors), although the hydraulic pump is a small part of the system energy wise, it's another moving part requiring maintenance etc (and in the Tbay example, they use vegetable oil rather than regular hydraulic fluids due to the risk of the oil entering the pool water.
Finally, rather than a standard 'pool' construction, to ensure the water dumped flows to the 'shore', the system can't pump water from the deep end, or else those pumps would be countering the effect - so the pool needs a water return, so that excess water at the shoreline can return back to the pumphouse.
I found this little graphic online that represents it well, and as you can see - large volumes of water return in a specially constructed channel, rather than just pipes like a pneumatic wavepool filtration system, to move large volumes. These channels, with their steel and concrete, naturally cost more to construct as well.
TL:DR - yeah, what @djrappa said.