Blindsight vs Darkness and Shadows of Moil

Question

How does a dragon's blindsight interact with a PC casting darkness or shadows of moil.

Would the PC get advantage on their attack rolls, and would the dragon get disadvantage on it's attack rolls?

Answer 1

Blindsight

can perceive its surroundings without relying on sight.

So effects like Darkness or Shadows of Moil would have no effect on the creature with Blindsight, because they are visual in nature.

There would be no PC advantage or dragon disadvantage.

Answer 2

Darkness creates "a heavily obscured area."

In an unofficial clarification on Twitter, Jeremy Crawford addressed the distinction between that and Shadows of Moil

Shadow of Moil heavily obscures you, full stop. The spell also dims the light around you. The fact that you're heavily obscured is a result of the flame-like shadows surrounding you, not the result of being in darkness. This means you're heavily obscured even to darkvision. #DnD

Heavy obscurement means:

A heavily obscured area—such as darkness, opaque fog, or dense foliage—blocks vision entirely. A creature effectively suffers from the Blinded condition (appendix A) when trying to see something in that area." (PHB, p. 183)

The Blinded condition means:

A blinded creature can’t see and automatically fails any ability check that requires sight; Attack rolls against the creature have advantage, and the creature’s Attack rolls have disadvantage. (PHB, App A)

This is how Darkness and Shadow of Moil work: by creating the Blinded condition in your foe. The wording is a little clumsy in my opinion (areas are obscured in rules, not people; blindness is not per-target in conditions text), but it's clear enough what they're saying.

However, "A creature with Blindsight can perceive its surroundings without relying on sight." A creature with Blindsight is still "blinded" by Darkness or Shadow of Moil, but they suffer no penalties from being blinded (within their blindsight radius.)

Because of this, Darkness and Shadow of Moil have no real effect on a creature with Blindsight. They blind it, but that doesn't matter. (There can be corner case exceptions, as with a deafened bat, or as the DM decides.)