One of the most underappreciated aspects of alternative energy analysis is ratio consideration. The viability of every concept is dependent on ratios like:

-gravimetric or volumetric energy density: energy per mass or volume (kJ/kg, kJ/m^3)
-resource energy density: how much energy is imbued per unit of resource
-capital economic production capacity: power per dollar (kW/$)
-thermodynamic efficiencies: how much useful electricity is produced per unit of resource processed
-actual utility factor: actual output under average operating conditions

The first point is pretty much encapsulated in "resource energy density". In the case of falling water or tidal water, a turbine is driven by water moving across a gravimetric pressure head. Basically water at a higher level pushes thru a turbine to reach a lower level. In a water fall (say Niagra falls) the pressure head is across a 50m fall. A kilogram of water at the top of the falls is imbued with 490J of energy (mass * 9.81N/kg * distance). Said kg of water would have an energy density of 490J/kg.

In the case of tidal power, tidal height is typically 6' (call it 1.8m) from low to high tide and you usually get two full periods per day. That means you get 4 crossings from high to low back to high and low. Notionally you should be able to extract energy in both directions if you have a reversible turbine or a turbine for each direction. That means a kg of water moving 1.8m has the potential to do 70J of work per day. I'm not sure what the rate of rainfall is, but that would work out a day production rate for a waterfall.

Anyways, 490J/kg is a whole lot bigger than 70J/kg which is probably why hydroelectrics typically involve waterfalls instead of tidal gadgets.

I'm going to glaze over capital analysis bit because I don't have enough data on the costs of steel, aluminum, or concrete. But it appears that natural gas is bar none the lowest cost method to spin a turbine for a simple reason: there is no heat exchanger needed to boil water into steam. Nat gas turbines burn the fuel and blast the exhaust thru the turbine just as a jet engine would. I can't imagine a simpler way to spin something save hydroelectrics, but a jet engine is a whole lot more dense in terms of space than a waterfall and the civil project supporting the generator.

Note: North America is installing more GJ of capacity of nat gas turbines than any other electrical production methods combined. IRC in 20 yrs over half of NA's nuclear plants will reach end of life. It takes roughly 8 years to build a nuke plant (two presidential mandates) and ground has not been broken on a single plant in decades.

Thermodynamic conversion efficiency: unfortunately every available joule doesn't end up as useful electricity. The zeroth law of thermodynamics rears it's entropic head and ends up defining things like best possible turbine efficiency. IRC, the best turbines can do is around 65% efficiency in driven or driving application. That really is a killer for pump storage methods. You lose 35% going one way and 35% going the other for a net loop eff' of 42%. Throw in generator losses and electrical transmission losses and you chisel away even more.

Actual utility factor is a number often significantly fudged in the alternative energy market. Look for power curves associated with wind turbines and you'll find that they tend to need a steady 18mph wind. Go much higher and they have to be shut down with blades turned into the wind (or they spin out of control). Go a little lower and their output plummets. The kinetic energy in moving masses (air included) is related to the square of velocity. Halve the velocity and the air has 1/4 of the energy. Even worse, wind turbine blades are optimized for narrow velocity regimes. Get below or above these regions and the compounded eff' and avail' energy drops output rapidly.

Meaningful public energy debates are terribly hobbled by a lack of very important vernacular. Most of the math is not very difficult (really more accounting than math), but not being able to compare capital cost per kW capacity makes most discussions irrational.