There is no such thing as a Reynolds equation, beyond the expression that defines it.
The Reynolds number arises from non-dimensionalizing the Navier-Stokes equations, which are a system of partial differential equations that model the velocity field of a fluid. It has some physical interpretations, some of which are very loose.
Turbulence is a physical phenomenon characterized by rapidly fluctuating, random (or, random appearing) velocities, the appearance of vortices, etc.
Turbulence is often associated with a high Reynolds number, but not always. For instance, any flow with a large characteristic length will typically have a high Reynolds number, but need not be turbulent.
I would imagine that, as far as aquarium flow, we would want the water to be well mixed, and with a relatively high velocity near the corals to bring nutrients to the corals and carry waste away - ie we want a certain number of the fluid particles, and what they carry, to impact a square inch of coral tissue at a certain rate.
A truly turbulent flow should always do that (as far as I understand, which may not be saying much), but I don't know that a power head or two set on random pulses actually produces a turbulent flow, or, more accurately, a turbulent flow throughout the tank. So I don't know if turbulent flow is the correct descriptor in the poll question. A laminar flow need not do it either (a gyre in a tank with no rocks will have low flow spots in the middle and corners).
Growth pattern considerations aside, a more random flow vs a more laminar flow I'd guess to be a toss up, as long as they accomplish what the "point" of high flow is.
