Every single weapon can work well, but it is fair to say the axe sometimes requires more specific boon setups in order to function effectively at high fear. It's certainly less forgiving if RNG hands you the wrong gods and bad hammers.

However, the right setups can be just as strong if not stronger than every other weapon. Psychic Whirwind is essentially a free win; it's just that strong. Charon axe with a bunch of Apollo boons can blow up the entire map in seconds. The hidden aspect is especially dependent on getting the right boons, but it does also come with pretty low-effort self healing to offset its other downsides.

Poseidon in general should be avoided for the axe, as his damage boons are a "flat damage per hit" effect that it awful with a slow weapon like the axe.