The Bug:

Wardens cannot detect "Flapping" vibrations from mobs, unlike Sculk Sensors.
This means they can't detect the movement of some mobs like Allays and Parrots as they move about, unless they hit the floor/land or bump into the Warden.
Meanwhile sensors are constantly triggered by the flapping of these mobs

A clear video of this behavior can be seen here:
WardenSculkFlapping.mp4

How to Reproduce:

1. Summon a Parrot and/or Allay next to some Sculk Sensors. Note how their flapping triggers them constantly
2. Try the same experiment but next to a Warden instead. The Warden will not hear these mobs flapping, and instead be triggered by other sources